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# Physics for Scientists and Engineers I (GT PH 141

CSU

GPA 3.64

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This 109 page Class Notes was uploaded by Giovanna Yost on Tuesday September 22, 2015. The Class Notes belongs to PH 141 at Colorado State University taught by Mingzhong Wu in Fall. Since its upload, it has received 13 views. For similar materials see /class/210314/ph-141-colorado-state-university in Physics 2 at Colorado State University.

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Date Created: 09/22/15

PH141 Fall 2011 Test Bank 1 Test version A or B mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET Last Name Initials Student ID DO NOT OPEN THIS EXAM BOOKLET UNTIL DIRECTED TO DO SO INSTRUCTIONS 1 WHEN DIRECTED TO DO SO FILL IN YOUR STUDENT NUlVIBER LAST NAME AND INITIALS ON THE BUBBLE SHEET DO THESE CLEARLY AND CAREFULLY ERRORS WILL RESULT N A BOUNCE FROM THE EXAM ROLLS MAIGE SURE TO MARK YOUR EXAM VERSION A OR B 2 WHILE THE EXAM IS OPEN BOOKAND OPEN NOTES 1N0 CALCULATORS OR ELETRONIC DEVICES OF ANY IQNDI YOU WOULD BE PRUDENT TO IGEEP THE USE OF THESE OPEN BOOK MATERIALS TO A MINIMUNI THESE ARE CONCEPT QUESTIONS THAT INVOLVE BASIC UNDERSTANDING AND A FEW IGEY EQUATIONS THERE IS ESSENTIALY VERY LITTLE THAT YOU CAN LOOK UP FROM YOUR BOOK OR NOTES THERE ARE ESSENTIALLY NO quotEQUATIONS TO FINDquot EXCEPT THE BASIC CONCEPT EQUATIONS YOU SHOULD HAVE IN YOUR HEAD THERE IS ALSO NOTHING THAT YOU SHOULD NEED A CALCULATOR FOR IT IS EXPECTED THAT YOU CAN DO BASIC ARITHIVIETIC INCLUDING POWERS OF TEN CALULATION S MANUALLY ANY NEEDED TRIG NUIVIERICS IS GIVEN BELOW 3 WHEN DIRECTED TO DO SO OPEN THIS BOOIQET AND BEGIN WORK IT IS RECOMMENDED THAT YOU WORKIN THIS BOOKLET AND WAIT UNTIL 10 MINUTES BEFORE THE END OF THE PERIOD TO MARK YOUR ANSWER SHEET MARK UP THE BOOKLET ANY WAY YOU LIIGE IT IS RECOMIMIENDED THAT YOU NOT WASTE TIVIE ERASING THIS IS A WORIG300K 4 NOTE THAT ERASURES ON THE BUBBLE SHEET CAN RESULT IN MISREADS AND LIACHINE GRADING ERRORS PLEASE LIAKE SURE OF YOUR ANSWER BEFORE MARIQNG THE BUBBLE SHEET 5 TEN MINUTES BEFORE THE END OF THE PERIOD YOU WILL BE REMINDED TO BEGIN TO WRAP THINGS UP AND MARK ANSWERS ON YOUR BUBBLE SHEET 6 FIVE MINUTES BEFORE THE END OF THE PERIOD YOU WILL BE REMINDED TO WRAP THINGS UP AND TURN IN YOUR BOOIQET AND ANSWER SHEET 7 THE EXAM HAS 12 QUESTIONS EACH QUESTION IS WORTH 9 POINTS THE MAXIMUNI SCORE IS 108 IT IS THE RAW SCORE THAT COUNTS SO YOU GET A quotSPOTquot OF 8 POINTS A PERFECT SCORE WILL NET YOU 108 POINTS TOWARD THE INTERM EXAM AVERAGE EG YOU CAN MISS 2 PROBLEMS AND STILL GET A MISS 3 AND STILL GET B etc ADDENDUM ON ACADEMIC INTEGRITY THE ACADEMIC INTEGRITY POLICY FOR THIS COURSE IS STATED BRIEFLY IN THE SYLLABUS AND IN DETAIL IN THE SEPARATE DOCUMENT POSTED ON RAMCT Failure to abide by these rules will be considered academic dishonesty and will be dealt with according to university policy For exams Exams are to be your own work and no consultation with other persons directly or indirectly is allowed You are not allowed to use any materials unless speci cally authorized to do by course policy or by the instructor It is never 39 39 to copy work from another student 1 Page 1 PH141 Fall 2011 Test Bank 1 Test version A or B mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET Possibly useful physics equations and connections Wherever needed take the gravitational acceleration parameter g as equal to 10 msz Derivative connections between 1D position xt velocity vxt and acceleration ax t d d axt va t vx t Exa Use slopes 1nstead of der1vat1ves whenever poss1b1e Integral connections between 1D position xt velocity vxt and acceleration ax t a sz V m Avxt j axtdt Axt j moan ammo mea Use areas instead of integration whenever possible Centripetal acceleration as for a point mass going around a circle of radius R with a speed v V2 a R Possibly useful math connections opposite COS adjacent opposite sin 39tan hypotenuse hypotenuse adjacent I sin30 1 2 cos 30 Jiz sin 30 cos 60 sin 60 cos 30 rule for complimentary angles sin45 JE21JE cos45 JE21JE tant9 sint9cost9 sm2t9cos2t9 1 2sin 9 cos 9 sin 26 d Der1vat1ve connect1on for xquot d xquot mc 1 x Page 2 PH141 Fall 2011 Test Bank 1 Test version A or B mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBl If the position xt for a 1D motion constant acceleration problem is given as xt x0 vot bot2 where x0 v0 and b0 are nonzero constants what is the acceleration a0 of the system TBl The position vs time curves for various lD motion scenarios are shown inthe gure Which curve or curves correspond to situations with zero acceleration The position vs time curves for various 1D motion scenarios are shown inthe gure Which curve or curves correspond to situations with negative velocity Time s TBl The position vs time curves for various 1D motion scenarios are shown inthe gure Which curve of curves correspond to situations with negative acceleration Tum s Page 3 PH141 Fall 2011 Test Bank 1 Test version A or B mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TR A 1D position vs time curves is shown to the right For which points is the Object moving away from the origin TBl A 1D position vs time curves is shown to the right For which points is the Object not moving at all TBl A 1D position vs time curves is shown to the right What is the physical signi cance of the area under the curve from A to The sign of the acceleration axt response for the xt graph to the right is Page 4 Position E Time sition E Time sition E Time PH141 Fall 2011 Test Bank 1 Test version A or B mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB The average velocity for travel from time II to time t for the xt graph to the right is Consider the xt response shown to the right Estimate the distance traveled between time t 0 and t 4 s TB Consider the xt response shown to the right What is the average speedbetween time t 0 and t 10 s Page 5 1 s 1 15 PH141 Fall 2011 Test Bank 1 Test version A or B mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB Consider the xt response shown to the right T m What is the average acceleration from t 20 s to h t 10 s 2 a 8llyr12 1415 7 n in ii di 77 A 7 TB An Object is moving along the Xaxis At time zero I 0 the Object is at position x0 and has a positive velocity vo1C At a later time taken as t T the Object has a velocity v11C 2v01C That is it s velocity has doubled If the Object is moving under a constant acceleration L101C during this motion which of the following mathematical statements is true TB An Object is moving along the Xaxis At time zero I 0 the Object is at position x 0 and has apositive velocity vo1C If the Object is moving under a constant negative acceleration L101C that is we have L101C lt 0 What is the travel time T for the Object to drop to zero velocity TB An Object is launched upward from ground level y 0 with a positive velocity voy at time t 0 The Object is moving under gravity de ned by the usual gravitational acceleration constant g Which of the following relations give the peak xposition ymp relative to y 0 attained a er the vertical launch Page 6 PH141 Fall 2011 Test Bank 1 Test version A or B mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB The Onedimensional motion of a particle is plotted in the gure What is the average acceleration in the interval BD 1 ms 15 TB The Onedimensional motion of a particle is plotted in the gure HOW far is the particle In ms from its starting point a er 8 s TBl John and Karen are jogging sidebyside on a trail in the woods at a speed of v0 Suddenly John sees the end of the trail and decides to speed up to reach it He accelerates at a constant rate of a While Karen continues on at a constant speed It takes a time period of At for John to reach the end of the trail When John reaches how far is Karen from the end of the trail TBl A rock dropped from a cliff covers 10 of its total distance to the ground in the last second of its fall Air resistance is negligible HOW high is the cliff Page 7 PH141 Fall 2011 Test Bank 1 Test version A or B mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB1 A rock dropped from a cliff covers X a ratio of its total distance to the ground in the last second of its fall Air resistance is negligible How high is the cli TB1 Ball A is dropped from the top of a building of height h at the same instant that ball B is thrown vertically upward from the ground When the balls collide they are moving in opposite directions and the speed of A is twice the speed of B At what time does the collision occur TB1 Ball A is dropped from the top of a building of height h at the same instant that ball B is thrown vertically upward from the ground When the balls collide they are moving in opposite directions and the speed of A is three times the speed of B At what time does the collision occur TB1 At time I 0 a particle located at the origin of a 2D x y system has a velocity 70 with 70 100 ms The vector 70 is oriented an angle 9 relative to the x axis of 30 such that the y component voy is positive The vector 70 is given by which of the following The and j39 denote the usual x y unit vectors respectively TB1 At time I 0 a particle located at the origin of a 2D x y system with a vector position 70 0 At this point in time it has a velocity 70 ms At a later time I 3 s the particle is located at located at 73 30 90 m and the velocity at this time and position is given by 73 12i3039 ms The and denote the usual x y unit vectors respectively Which vector below describes the average velocity during this 3 second interval TB1 At time I 0 a particle located at the origin of a 2D x y system with a vector position F0 0 At this point in time it has a velocity 70 3 ms At a later time I 3 s the particle is located at located at 73 30 90 m and the velocity at this time and position is given byx73 12i3039 ms The f and denote the usual x y unit vectors respectively Which vector below describes the average acceleration during this 3 second interval Page 8 PH141 Fall 2011 Test Bank 1 Test version A or B mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET Human blood contains various discrete objects that can be separated in a centrifuge as shown to the right What is the period of the rotation T time in seconds to go around once for a rotation rate of 3600 rpm TB Human blood contains various discrete objects that can be separated in a centrifuge as shown to the right Assume that you have properly converted the rotation rate of 3500 rpm to the period of the rotation T time in seconds to g 0 around once Label the largest rotation radius the bottom end of the test tube as RW1X lnterms of T and Rm1X what is the centripetal acceleration of the particles at the bottom of the test tube TBl Human blood contains various discrete objects that can be separated in a centrifuge as shown to the right We know that particles in the blood experience a centripetal acceleration that is always inward toward the axis of rotation If you were a DNA molecule inside one of these particles which way would you experience a force TBl The hunter in the gure res a dart at the monkey in the tree and simultaneously e g at time t 0 the monkey lets go of the branch and falls Note that the hunter aims right at the monkeyAssume all the parameters shown in the diagram are known except for the vertical position y at which the dart strikes the monkey Which expression below gives the time t rm at which the dart strikes the monkey Page 9 PH141 Fall 2011 Test Bank 1 Test version A or B mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB The hunter in the gure res a dart at the monkey in the tree and simultaneously e g at time t 0 the monkey lets go of the branch and falls Note that the hunter aims right at the monkeyAssurne all the parameters shown in the diagram are known except for the vertical position y at which the dart strikes the monkey Which expression below gives the time t rm at which the dart strikes the monkey TBl The hunter in the gure res a dart at the monkey in the tree and simultaneously e g at time t 0 the monkey lets go of the branch and falls Note that the hunter aims right at the monkeyAssurne all the parameters shown in the diagram are known except for the vertical position y at which the dart strikes the monkey Assume now that the dart ring speed is such that the hit point is at y h eg the hit is just at the same vertical position as the launch point for the dart In this case which expression below for the hit time 1 is true TBl Consider the clifflaunch trajectory to the right The launch is at time t 0 urne that all the parameters shown in the diagram are known and that R satis es the expression derived in Tipler and Mosca Problem 393 What is the height of the trajectory above the launch point TBl Consider the clifflaunchquot trajectory to the right The launch is at time t 0 Assume that all the parameters shown in the diagram are known and that R satis es the expression derived in Tipler and Mosca Problem 393 If the launch angle is quotstraight out that is at 80 0 what is R Hint Work the problem from the basic considerations for a falling Object and velocity times time Page 10 PH141 Fall 2011 Test Bank 1 Test version A or B mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB Consider the quotwall bouncequot trajectory to the right 7 The launch is at time t 0 Work wi e 6339 ff parameters in the diagram and take the gravitational l acceleration parameter g equal to 10 msz At I what time t tW will the ball strike the wall v n 10 115 to ms I 20 m 1 397 1 40 m 7 v TBl Consider the quotwall bouncequot trajectory to the right j r The launch is at time t 0 Work wi e 0 39 g 1 parameters in the diagram and take the gravitational r acceleration parameter g equal to 10 msz How x far call this distance L from the wall will the ball again reach the 2 m corrected from initial 139 m mS version height of the launch point NOT the ground I m ms J 20 m 7 40 m7 Darlence is a stunt motorcyclist in a traveling circus For the climax of her show she takes off from the ramp at angle 80 clears a ditch ofwidthL and lands on an elevated ramp height h onthe other side See the gure to the right For a given takeoff speed v nd the maximum height hmax allowed to make the jump successfully Page ll PH141 Fall 2011 Test Bank 1 Test version A or B mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET Darlence is a stunt motorcyclist in a traveling circus For the climax of her Show she takes off from the ramp at angle 8 clears a ditch ofwidthL and lands on an elevated ramp height h onthe other side See the gure below For a given takeoff speed v nd the maximum width Lmax allowed to make the jump successfully TBl A 10kg object on a frictionless table is subjected to two I horizontal forces 1 and 132 with magnitudes of F1 10 N i and F2 20 N as shown Findthe third horizontal force 133 that must be applied so that the object is in static equilibrium TBl A 10kg object on a frictionless table is subjected to two horizontal forces 151 and 172 with magnitudes of F1 15 N and F2 20 N as shown Findthe third horizontal force 153 that must be applied so that the object is in static equilibrium TBl A 10kg object on a frictionless table is subjected to two horizontal forces 151 and 172 with magnitudes of F1 1 N and F2 2 N as shown Find the third horizontal force 173 that must be applied so that the object is in static equilibrium Page 12 PH141 Fall 2011 Test Bank 1 Test version A or B mark this version on your answer sheet YOU MUST RETURN THrs EXAM BOOKLET WITH YOUR ANSWER SHEET TB Your car is stuck in a mud hole You are alone but you have a long strong rope Having studied physics you tie the rope tautly to a telephone pole and pull on it sideways as shown in the gure Find the tension T in the rope when the angle Bis 30 and you are pulling with a force F Of400 N the car does not move TBl Your car is stuck in a mud hole You are alone but you have a long strong rope Having studied physics you tie the rope tautly to a telephone pole and pull on it sideways as shown in the gure below Find the tension T in the rope when the angle Bis 3 and you are pulling with a force F OflOO N the car does not move TBl A 20kg box rests on a frictionless ramp with a slope of 15 A mover applies a force F at an angle of 4000 to the horizontal in order to pull the box up the incline as shown in the gure What is the smallest force F that the mover will have to apply for the box to move up the ramp Where needed take the gravitational acceleration parameter g as equal to 10 msz TBl A 20kg box rests on a frictionless ramp with a slope of 15 A mover applies a force F at an angle of 4000 to the horizontal in order to pull the box up the incline as shown in the gure A physics student explains to the mover that 4000 is not the 39 um angle to move the box with the smallest value OfF What is the best angle to the horizontal to move the box with the smallest possible force Page 13 5U39 PH141 Fall 2011 Test Bank 1 Test version A or B mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBl TWO hanging masses and one horizontal mass on a frictionless surface are connectedto ropes over massless frictionless pulleys as shown Take the le rope tension as T L the right rope tension as T R and the common acceleration no of the masses m1 m2 and m as up to the right and down respectively Take T L and T R as positive quantities 39ch quotF ma equation below applies to the system as a Whole TBl TWO hanging masses and one horizontal mass on a frictionless surface are connectedto ropes over massless frictionless pulleys as shown Take the le rope tension as T L the right rope tension as T R and the common acceleration no of the masses m1 m2 and m1 as up to the right and down respectively Take T L and T R as positive quantities Which quotF ma equation below applies to the hanging mass m1 TBl TWO hanging masses and one horizontal mass on a frictionless surface are connectedto ropes over massless frictionless pulleys as shown Take the le rope tension as T L the right rope tension as T R and the common acceleration no of the masses m1 m2 and m as up to the right and down respectively Take T L and T R as positive quantities What is the acceleration of the system Page 14 PH141 Fall 2011 Test Bank 1 Test version A or B mark this version on your answer sheet YOU MUST RETURN THrs EXAM BOOKLET WITH YOUR ANSWER SHEET TBl Two masses supported on Opposite inclines with frictionless surfaces are connected by a massless xed length rope that hangs over a ictionless massless pulley as shown Take the le mass as mL 8 kg and the right mass as mg 10 kg Take the value Of the common acceleration for the two masses as go Where needed take the gravitational acceleration parameter g as equal to 10 msz Which expression below will give the numerical value Of a0 TBl Two masses supported on Opposite inclines with frictionless surfaces are connected by a massless xed length rope that hangs over a ictionless massless pulley as shown Take the le mass as mL 8 kg and the right mass as mg 10 kg Take the value Of the common acceleration for the two masses as no Which way does the system accelerate TBl Two masses supported On Opposite inclines with frictionless surfaces are connected by a massless xed length rope that hangs over a ictionless massless pulley as shown Take the le mass as mL 8 kg and the right mass as mg 10 kg Take the value Of the common acceleration for the two masses as no What is the normal force F1905 Of the right incline On mass m R TB 439 u 5 Abullet Ofmass m3 100 g not kg at aninitial speed VB 100 ms hits abale thay and de accelerates at a uniform rate such that it comes to rest a er a distance D 05 In What is the magnitude Of the deacceleration rate a B Page 15 PH141 Fall 2011 Test Bank 1 Test version A or B mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TR A bullet ofmass m3 100 g not kg at an initial speed VB 100 ms hits a bale ofhay and de accelerates at a uniform rate to rest in a distance D 05 In What is the stopping time T B for the bullet TBl Abullet ofmass m3 100 g not kg at aninitial speed VB 100 ms hits abale ofhay and de accelerates at a uniform rate to rest in a distance D 05 In What is the deacceleration force F B quotfeltquot by the bullet TBl Two separate stacks of masses each with ve washers of mass m are suspended on opposite sides of a ictionless massless pulley as indicated When one washer is removed the ve washer side accelerates down and the four washer side accelerates up with an acceleration a0 What is no TBl Two separate stacks of masses each with ve washers of mass m are suspended on opposite sides of a ictionless massless pulley as indicated For this in balance state what is the tension T R in the rope a TR10mg c TRmg b TR5mg d TR0 Page 16 3 5m 5m 5 PH141 Fall 2011 Test Bank 1 Test version A or B mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET Two separate stacks of masses each with ve washers of mass m are suspended on opposite ETQ sides of a frictionless massless pulley as indicated A When one washer is removed the rope changes from its inbalance tensionvalue to some new T R and the system accelerates What is T R 3 5m 5m 3 TBl Masses m and 2m are on ahorizontal frictionless surface connected by a massless rope r7 and pulled on the left and right Sides w1th 39 opposing horizontal forces I71 and 172 as indicated We denote the positive magnitudes of 171 and 132 as F1 and F 2 respectively You may take the rope tension force as T R and the acceleration to the right as no What is TR TB Masses m and 2m are on ahorizontal frictionless surface connected by a massless rope and pulled on the left and right Sides With 7 opposing horizontal forces I71 and 172 as indicated We denote the positive magnitudes of 171 and 172 as F1 and F 2 respectively You may take the rope tension force as T R and the acceleration to the right as no What is no TBl Masses m and 2m are on ahorizontal frictionless surface connected by a massless rope r r and pulled on the left and right sides with opposing horizontal forces 171 and 172 as indicated We denote the positive magnitudes of 171 and 152 as F1 and F2 respectively Assume now that both F1 and F2 increase with time according to F1 Ct and F2 20 where C is a positive constant What happens to the tension in the rope as time advances Page 17 PH141 Fall 2011 Test Bank 1 Test version A or B mark this version on your answer sheet YOU MUST RETURN THrs EXAM BOOKLET WITH YOUR ANSWER SHEET TB A block of mass m slides at constant speed down aplane inclined at an angle of Bto the horizontal Constant speed requires which friction force f from the list below TB Ablock of mass m slides at constant speed down a plane that makes an angle of Bwith the vertical direction not the horizontal It follows that TB The coef cient of kinetic friction between the tires of a car taken as a whole 7 not one at a time and a at horizontal asphalt road is 010 Neglecting air resistance what is the magnitude of the maximum deceleration amax Ofthe car when it is braked so that the wheels lock up before the tires blow of course Where needed take the gravitational acceleration parameter g as equal to 10 msz TB The coef cient of kinetic friction between the tires of a car taken as a whole 7 not one at a time and a at horizontal asphalt road is 050 Neglecting air resistance what is the shortest distance D that it will take the car to stop a er the brakes are applied and the wheels lock up if it is initially traveling at 10 ms Where needed take the gravitational acceleration parameter g as equal to 10 msz TB The coef cient of kinetic friction between the tires of a car taken as a whole 7 not one at a time and a at horizontal asphalt road is 050 Neglecting air resistance what is the shortest time T that it will take the car to stop a er the brakes are applied and the wheels lock up if it is initially traveling at 10 ms Where needed take the gravitational acceleration parameter g as equal to 10 msz block of mass m rests on a horizontal table as shown The block is pulled by a massless rope with a force 17 at an angle 8 The coef cient of kinetic friction is Mr The mass is m and the rope pulling angle to the horizontal is 8 If the magnitude of the force F is adequate to move the block what expression below gives the net horizontal force Hint Remember your trig Page 18 PH141 Fall 2011 Test Bank 1 Test version A or B mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET A block Of mass m rests on a horizontal table as shown The block is pulled by a massless rope with a force 1 at an angle 8 The coef cient Ofstatic friction is 5 05 Ifone has m 3 kg and 8 45 what is the minimum value Ofthe force needed to move the block Where needed take the gravitational acceleration parameter g as equal to 10 msz A block Of mass m rests on a horizontal table as shown The block is pulled by a massless rope with a force 1 at an angle 8 Ifthe minimum value Of the force needed to move the block is Fmin what is the coef cient Of static friction TBl A car is going around a circular banked curve racetrack at a speed v ignore the 40 kmh number in the gure and a curve radius R center Of track Off to the right somewhere as indicated schematically in the gure Take the mass Ofthe car asM Treat the car as a block sliding around the track on a frictionless surface What speed is required for the car to go around without 1 m kmh sliding up or down the banked track TBl A car is going around a frictionless circular banked curve racetrack at a speedv ignore the 40 kmh number in the gure and a curve radius R center Of curvature track to the right Of the car horizontal somewhere as indicated schematically in the gure Take the mass Of the car as M Which equationbelow describes the vertical equilibrium condition Page 19 PH141 Fall 2011 Test Bank 1 Test version A or B mark this version on your answer sheet YOU MUST RETURN THrs EXAM BOOKLET WITH YOUR ANSWER SHEET TB A car is going around a circular banked curve racetrack at a speed v ignore the 40 kmh number in the gure and a curve radius R center Of track Off to the right somewhere as indicated schematically in the gure Take the mass Ofthe car asM Treat the car as a block sliding around the track on a frictionless surface Which equation below describes the horizontal quotF ma condition for circular motion TB A car is going around a circular banked curve racetrack at a speed v ignore the 40 kmh number in the gure and a curve radius R center Of track Off to the right somewhere as indicated schematically in the gure Take the mass Ofthe car asM The track has friction and the car is going around without sliding If the velocity Of the car increases to the point where the car starts to slide up the banked incline which way will the friction force On the car be directed TB A car is going around a circular banked curve racetrack at a speed v ignore the 40 kmh number in the gure and a curve radius R center Of track Off to the right somewhere as indicated schematically in the gure Take the mass Ofthe car asM The track has friction and the car is going around without sliding If the velocity decreases to the point where the car starts to slide down the banked incline which way will the friction force on the car be directed u z rum1 r kan1h TB Consider a rod with a length L and a linear mass density given as Ax Ax and a total mass M In other words a differential part Of the rod Of length dx located at position x will have a mass dm equal to Axdx or Axdx Which equation below gives the total mass Of the rod TB Consider a rod with a length L and a linear mass density given as Ax Ax and a total mass M In other words a differential part Of the rod Of length dx located at position x will have a mass dm equal to Axdx or Axdx Which equation below gives the center Of mass Of the rod Page 20 PH141 Fall 2011 Test Bank 1 Test version A or B mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBl Consider a rod with a length L a uniform density and a mass M One places a large heavy but small Object of mass 3M on one end of the rod Where is the center of mass of this rodplus mass located T Bl Consider the Atwood machine with a heavy mass ml and a lighter mass m 2 as shown The rope is massless When released mass ml V 7 F will accelerate down and mass m 2 will accelerate up For the 3 purposes Ofthis problem take the mass Ofthe pulley m to be zero What is the acceleration an of the massropemass system when released T Bl Consider the Atwood machine with a heavy mass ml and a lighter mass m 2 as shown The rope is massless When released mass m1 V 7 F will accelerate down and mass m 2 will accelerate up For the 3 purposes Ofthis problem take the mass Ofthe pulley m5 to be zero Take the acceleration an of the massropemass system as known easily Obtained from quotF ma for the system In terms of an and the masses which expressions below for the rope tension T is are correct TBl Consider the Atwood machine with a heavy mass m1 and a lighter I mass m 2 as shown The rope is massless When released mass m1 Dr 7 will accelerate down and mass m 2 will accelerate up For the J purposes Ofthis problem take the mass Ofthe pulley m5 to be zero Take the acceleration an of the massropemass system as known Assume that the masses are released from the same height which we will call y 0 and take the positive y direction to be up Which expression below gives the centerOf mass position of the system Page 21 PH141 Fall 2011 Test Bank 1 Test version A or B mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB What are the fundamental units in terms of the kg m and s only of the spring constant k de ned through the Hooke s Law force equation F 7kx You will need to invoke the fundamental units of force to extract the units of k TB What are the fundamental units in terms of the kg m and s only of the derived unit of force the Newton N A good working equation for this is our friend quotF ma quot TB Two objects have different masses and different speeds For mass 1 the mass is twice that of mass 2 But the speed ofmass 1 is halfthe speed ofmass 2 What is the ratio oftheir kinetic energies that is what is the numerical value of K 2 Kl where K is the usual symbol for kinetic energy and the subscripts l and 2 refer to objects 1 and 2 respectively TB The mass ofthe earth is 6x10 kg The radius ofthe earth s orbit aroundthe sun is about 15x10ll m The period ofthe orbit is of course one year which you may round off to 3x107 seconds Estimate the kinetic energy of the earth s motion around the sun For this numerical exercise you may take 7 1 10 TB Drop two masses ml and m 2 from some height 11 above the ground Just before they hit the ground what is the ratio of their kinetic energies TB Consider a projectile that is launch from a cannon and takes the usual type of trajectory that goes to some maximum height then falls back down and hits the ground while at the same time traveling horizontally for some range distance Is the kinetic energyK larger at launch time and the peak of its trajectory or at the hit time TB A 20kg particle moving along the x axis has a velocity of 20 ms as it passes through the origin It is subjected to a single force FX that varies with position as shown in the gure What is the kinetic energy of the particle when it is at F40 m Page 22 PH141 Fall 2011 Test Bank 1 Test version A or B mark this version on your answer sheet YOU MUST RETURN THrs EXAM BOOKLET WITH YOUR ANSWER SHEET TB A 20kg particle moving along the x axis has a velocity of 20 ms as it passes through the origin It is subjected to a single force FX that varies with position as shown in the gure What is the speed of the particle when it is at F40 m N u 4 u a TB A 20kg particle moving along the x axis has a I velocity of 20 ms as it passes through the origin It is subjected to a single force Fx that varies with position as shown in the gure What is the speed ofthe particle when it is at F20 m TB A particle moving along the x axis is subjected to a single varying force Fx102x N What is the work done by this force when the particle moves from F0 to F20 m TB A particle moving along the x axis is subjected to a single varying force FX103xZ N What is the work done by this force when the particle moves from F0 to F20 m TB Aparticle moving along the x axis is subjected to a single varying force Fx2x4 N What is the work done by this force whenthe particle moves from F0 to F40 m TB A 20kg block slides 10 m down a frictionless incline that makes an angle of 30 with the horizontal What is the total work done on the block TB A 20kg block slides 10 m down a frictionless incline that makes an angle of 30 with the horizontal What is the increase in the kinetic energy of the block after it has slid 10 m Page 23 PH141 Fall 2011 Test Bank 1 Test version A or B mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB1 Particle a has mass m is initially located on the positive x axis at xx0 and is subject to a repulsive force Fx from particle b The location of particle b is xed at the origin The force Fx is inversely proportional to the square of the distance x between the particles That is Fx Axz where A is a positive constant Particle a is released from rest and allowed to move under the in uence of the force What is the kinetic energy of Particle a when it passes x2x0 TB1 Particle a has mass m is initially located on the positive x axis at xx0 and is subject to a repulsive force Fx from particle b The location of particle b is xed at the origin The force Fx is inversely proportional to the square of the distance x between the particles That is Fx Axz where A is a positive constant Particle a is released from rest and allowed to move under the in uence of the force What is the speed of Particle a when it passes szo TB1 Particle a has mass m is initially located on the positive x axis at xx0 and is subject to a repulsive force Fx from particle b The location of particle b is xed at the origin The force Fx is inversely proportional to the square of the distance x between the particles That is Fx Ax where A is a positive constant Particle a is released from rest and allowed to move under the in uence of the force What is the kinetic energy of Particle a when it passes x2x0 TB1 Particle a has mass m is initially located on the positive x axis at xx0 and is subject to a repulsive force Fx from particle b The location of particle b is xed at the origin The force Fx is inversely proportional to the square of the distance x between the particles That is Fx Ax3 where A is a positive constant Particle a is released from rest and allowed to move under the in uence of the force What is the speed of Particle a when it passes szo TB1 A 20kg particle is given a displacement of A 30 mi30 mj39 l0 ml During the displacement a constant force I 20 Ni l0 Njl0 NH acts on the particle What is the work done by I for this displacement TB1 A 20kg particle is given a displacement of A 30 mi 40 ml During the displacement a constant force it 20 Ni l0 Njl0 NM acts on the particle What is the work done by I for this displacement TB1 Page 24 PH141 Fall 2011 Test Bank 1 Test version A or B mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET A 20kg particle is given a displacement of A 50 m 50 ml During the displacement a constant force 15 10 Nf20 Nj10 NH acts on the particle What is the work done by 15 for this displacement Page 25 PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET Student 1 legible Name legible Section 01 or 02 1 A Fill in your student number last name and initials on the bubble sheet Do these clearly and carefully Errors will result in a rejected bubble sheet B Mark your exam version A or B C Hand write in your section number 001 or 002 in the section block on the bubble sheet D Fill in your name and section number on the exam booklet 2 While the exam is open book and open notes gno calculators or eletronic devices of any kind 1 you would be prudent to keep the use of these open book materials to a minimum These are concept questions that involve basic understanding and a few key equations There is essentially very little that you can look up from your book or notes There are essentially no quotequations to fmd quot You should have the basic concept equations in your head 3 It is recommended that you work in this booklet and wait until 10 20 minutes before the end of the period to mark your answer sheet Mark up the booklet any way you like It is recommended that you not waste time erasing This is a workbook 4 Make sure to use a soft 2 pencil to fill in the ovals on the bubble sheet Note that erasures 011 the bubble sheet can result in misreads and machine grading errors Please make sure of your answer before marking the bubble sheet 5 Ten minutes before the end of the period you will be reminded to begin to wrap things up and mark answers on your bubble sheet 6 Five minutes before the end of the period you will be reminded to wrap things up and turn in your booklet and answer sheet 7 The exam has 15 questions Each question is worth 7 points The maximum score is 105 It is the raw score that counts So you get a quotspotquot of 5 points A perfect score will net you 105 points toward the in terrn exam average Eg you can miss 2 problems and still get an A miss 3 and still get B miss 5 and still get a C etc Addendum on academic integrity the academic integrity policy for this course is stated brie y in the syllabus and in detail in the separate document posted on RamCT Failure to abide by these rules will be considered academic dishonesty and will be dealt with according to university policy For exams exams are to be your own work and no consultation with other persons directly or indirectly is allowed You are not allowed to use any materials unless speci cally authorized to do by course policy or by the instructor It is never acceptable to copy work from another student Page 1 PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET Possibly useful physics equations and connections Wherever needed take the gravitational acceleration parameter g as equal to 10 msz Derivative connections between 1D position xt velocity vxt and acceleration ax t d d axt Ema vx t Exa Use slopes 1nstead of der1vat1ves whenever poss1b1e Integral connections between 1D position xt velocity vxt and acceleration ax t a sz v M1 Avxt j axtdt Axt j moan ammo mea Use areas instead of integration whenever possible Centripetal acceleration ac and centripetal force F 5 both inward for a point mass m going v2 mv2 around a c1rc1e ofradlus R w1th a speed V a Fc R Newton s First Law An object in motion constant velocity tends to stay in motion same velocity d d 2 Newton s Second Law F ma m V m x dt d Newton s Third Law For every force applied toin a system there is an equal and opposite force action reaction Hooke s law spring force law F kx end xend Work force acting over a distance W I F d Fquot in 1D I dex Fmg gtlt distance start Xmm 1 Kmetlc energy K Emv2 Gravity work ngv mgh 1 Sprmg work Wsprmg Ekx2 en a 1 1 Work 7 kinetic energy theorem work on a free mass I F d Fquot mv62nd mv m start 2 2 Maximum static friction force F SE39 motion uan stationary mass Kinetic friction force Fkinetic faction uan moving mass d 2 d d d Momentum de ned from quotF maquot F m x m V mv pp mv d dt dt dt d quotF maquot and actlonreact1on bas1s for momentum conservatlon 1 F 7p 3 dp Fair 1 means that a force F1 acting over an incremental time dt on an object 1 causes a change in momentum dp for object 1 2 Action reaction says that the object 2 providing this force Page 2 PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET suffers an equal and opposite force namely F 2 F1 and this force is applied for the same dt We have therefore dpz dp1 Elastic collisions momentum and kinetic energy are conserved in 1D the speed of approach for the oncoming masses in atwo mass collision equals the speed separation after the collision Inelastic collisions momentum is conserved but energy is not conserved Rotational dynamics based on TM and standard notation SRt9dSdtv Rdt9dtRa a Salt2 Ral2t9alt2 Rda2dtRa Torque for forces perpendicular to the lever arm pivot line etc 139 RF I a rotational analog to F ma Moment of inertia Mass on the end ofa massless rod I MR2 Rimmed wheel all mass uniformly distributed around circumference I MR2 Rod of length L and mass M rotating about an axis at one end and perpendicular to the rod I l 3ML2 Uniform disk of radius R and mass M rotating about an axis through the center and perpendicular to the disk I l 2MR 2 Torque and angular momentum vector connections 3 17 X R I0 dEdt E 17 X 27 IE The vector cross product gtlt 6A3 direction of 21 X R by right hand rule Universal gravitation force law F12 Gmlmg r122 attractive ithis is a concept equation Gravitational potential energy Ur of a point mass m in the gravitational field of a uniform spherical shaped object of mass M at a distance r away from the center and with U taken as zero at roo Ur GMmr Effective gvalue at the surface of a planet g GM R 2 Energy balance for the escape velocity vm of a mass m launched from the surface of a uniform 1 GM spher1cal planet of mass M and rad1us R Emvgsc Tm Solid angle rules for hollow or variable density spheres with spherical symmetry All mass elements outside the radius r of the observer yield a net g value of zero How do F ma and Hooke s Law F kx combine to give harmonic motion that is with x x0 sina0t mo Vkm etc Frequency and period connections m0 27239f0 f0 lTO f0 m0 27239 etc do you see the connections Harmonic motion connections x x0 sin mot vx xowo cos mot ax x0ag sin mot etc Page 3 PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET Harmonic motion and phase How can xt x0 cosa0t 5 xt x0 sina0t and xt xc cosa0t xs sina0t all be equivalent How do 139 Ia and the restoring force dynamics for a pendulum made of a light string of length L and a mass m combined with the small angle approximation sin 9 m 9 yield small angle harmonic motion 9 60 sin mot mo lg L etc How does pendulum motion in accelerated reference frames work For linear accelerated motion For circular motion For accelerated motion down an incline Answer If there is an 5 the accelerated system feels an effective gravity ge 5 in addition to any regular g that might be present sm sm Transverse harmonic wave yxt A cos kx wt or cos 27239i Zn39L etc etc A T Velocity for a wave v if wk d2yxt l d2yxt 7 Transverse wave equation v2 alt2 Doppler effect concept equation 7 useless without understanding fIeceiver some Vair T receiver f Vair some Perfect gas law PV nRT NkBT gm V2 W temperature kinetic energy Absolute zero temperature To 0 K m 27315 C Thermodynamic internal energy point atom with three translational degrees of freedom Emt Nmvz NkBT nNA gkgr nRT Gas constant Boltzmann constant connection R N Akg 2 Normalized Boltzmann speed distribution f v i jvz e K I ZkBT 2kg Degrees of freedom 7 energy connection For any energy form such as mv mv or mvz2 translational kinetic energy 1xm or Iya rotational kinetic energy kx2 and Llu spring potential and kinetic energy etc Boltzmann averaging gives mv2gt kBT etc Gas constant value R 0083 Latmmol K 8314 Jmol K when to use which one Speci c heats and thermodynamic internal energy Ejm CVT in K n1ch nc39VT understand the notation too First law of thermodynamics One version AEim Qquot W0n Another version Qquot AEim Wby Why do these say the same thing Internal energy of an ideal gas Eim CVT why Why does the specific heat at constant volume always apply to the internal energy Speci c heat at constant pressure Qquot AEintPAV MAT nRAT nc RAT c39P c R Page 4 PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET Adiabatic expansion QM 0 PV nRT differential analysis and integration gives PV const y CP CV For a monatomic ideal gas we have cl R and cvp R so we also have y 53 2 2 Thermodynamic work Why IPdV Won JPdV 1 1 Work done for single legs in simple perfect gas thermodynamic PV cycles Constant volume W 0 why Constant pressure Why P V ml Win01 why V mj dV Isothermal T wrist Why nRT J why sznal V Adiabatic QM 0 Why CVAT why Ef ciency of a reversible thermodynamic engine 8 1 Q0 Qm Ef ciency of a Carnot engine 8 1 TC TH Coefficient of performance for a refrigerator COP W on Possibly useful math connections oppos1te 08 2 adjacent nan oppos1te hypotenuse hypotenuse ad acent sin30 1 2 cos 30 52 sin 30 cos 60 sin 60 cos 30 rule for complimentary angles sin45 J 21JE cos45 J 21J tant9 singc056 sin2t9c052t9 1 25in 9 cos 9 sin 26 sin A B sin Acos B cosA sin B get sinA B from symmetry sin sin 61 sin 62 2cost91 62sint91 62 d Der1vat1ve connectlon for xquot d xquot men 1 x Circumference of a circle C 2727 Area ofa circle A In2 Area ofa sphere A 47239quot2 Volume of a sphere V 37273 Isin d cost9jcost9dt9 sint9 Page 5 PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET Disclaimer This test bank is provided to the student as a guide only The problems below have not been totally vetted and may contain errors and ambiguities They are intended only to give the student an idea of the genre of problems they may expect on the exam Final exam problems will be drawn from this test bank and all previous test banks 1 3 for the course Once this test bank is posted speci c questions on these problems will not be entertained Feedback on any possible errors and ambiguities of course is welcoe Good luck on the fmal exam Page 6 PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB4 On the Reaumur temperature scale the melting point of ice is 0 R and the boiling point of water is 80 R What is the expression for converting temperatures on the Reaumur scale IR to the Celsius scale tc TB4 On the Reaumur temperature scale the melting point of ice is 0 R and the boiling point of water is 80 R What is the expression for converting temperatures on the Reaumur scale IR to the Fahrenheit scale t1 TB4 A thermistor is a solidstate device widely used in a variety of engineering applications Its primary characteristic is that its electrical resistance R varies greatly with temperature T Its temperature dependence is given approximately by R 100e200T Which of the following statements is true TB4 The fractional distribution function of molecular speeds in a gas is f v Which of the following integrals gives the average speed of the molecules TB4 The fractional distribution function of molecular speeds in a gas is f v Which of the following integrals gives the mean square speed of the molecules TB4 Equal amounts of heat are transferred to two objects A and B If the mass of object A is twice that of object B and the specific heat of object A is one third ofthat of object B how do the subsequent changes in their temperatures compare TB4 Object A has a mass that is twice the mass of object B and object A has a speci c heat that is four times of the speci c heat of object B If the two objects have the same amount of increases in temperature how do the amounts of heat transferred to the objects compare TB4 Object A has a mass that is twice the mass of object B and object A has a speci c heat that is three times of the speci c heat of object B If equal amounts of heat are transferred to these two objects how do the subsequent changes in their temperatures compare Page 7 PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB4 A gas may change its state according to different quasi p static paths or combinations Of paths shown in the A 13 gure Which Of the following statements is WRONG D39 C V TB4 A gas may change its state according to different quasi p static paths or combinations Of paths shown in A 3 gure For which path is the work done on the gas by the external world positive 0 C V TB4 A gas may change its state according to different quasi P static paths or combinations Of paths shown in the A 3 gure The work done on the gas by the external world is D C V TB4 For purposes Ofthese numerics take the speci c heat Ofice as 2 kJkg K the heat Of fusion for ice as 300 kJkg and the speci c heat Ofwater as 4 kJkg K How much heat energy QM is required extracted or added to take 100 g Of water at 50 0C freeze it and lower the temperature Ofthe ice to 100 C TB4 For purposes Ofthese numerics take the speci c heat Ofice as 2 kJkg K the heat Of fusion for ice as 300 kJkg and the speci c heat Ofwater as 4 kJkg K How much heat energy QM is required extracted or added to take 100 g Ofice at 100 0C warm it up melt it and raise the temperature Of the water to 50 C Page 8 PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB4 If a person is accidentally exposed to a blast of water vapor steam at 100 OC heshe can be burned severely A blast of hot air on the other hand will have much less of an effect Why TB4 If 100 J of heat is extracted from a system at the same time that 100 J ofwork is done on the system what is the energy change of the system AEim TB4 If 100 J of heat is added to a system at the same time that 100 J of work is done on the system what is the energy change of the system AEim TB4 If 100 J of heat is added to a system at the same time that 200 J of work is done by the system what is the energy change of the system AEim TB4 Two identical blocks each of mass mblock are rubbed together to produce heat The speci c heat of the blocks is specified as cblmk in Jkg K Take the normal force pressing the blocks together as Fquot inN the coefficient of kinetic friction as uk and the average relative speed of the rubbing motion as vmb Which equation below gives the heating power Phea ng generated from the rubbing process assuming that all of the nonconservative friction work goes into heat Note Not all of the parameters specified above may be needed to obtain Phea ng TB4 Two identical blocks each of mass mblock are rubbed together to produce heat The speci c heat of the blocks is specified as cblmk in Jkg K Take the normal force pressing the two blocks together as Fquot inN the coefficient of kinetic friction as uk and the average relative speed of the rubbing motion as vmb Which equation below gives the rate of increase in the block temperatures assumed the same taken as dTblock dt generated from the rubbing process assuming that all of the nonconservative friction work goes into heat Note Not all of the parameters specified above may be needed to obtain dTblock dt Page 9 PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB4 The figure tO the right shows a PV diagram for a P reversible quasistatic two leg gas compression process The gas starts out at point Pi Vi The gas is first heated at constant volume V so that the pressure is increased Path A PW vr from some P tO some higher value Pf Call this intermediate point Pf Vi The gas is then compressed at constant pressure Pf tO a final volume Vf The pi V1 final state is at Pf Vf At what point or points is the temperature the highest TB4 The figure tO the right shows a PV diagram for a P reversible quasistatic two leg gas compression process The gas starts out at point Pi Vi The gas is first heated at constant volume V so that the pressure is increased Path A PW Vr from some P tO some higher value Pf Call this intermediate point Pf Vi The gas is then compressed at constant pressure Pf tO a final volume Vf The P V final state is at Pf Vf At what point or points is the temperature the lowest TB4 The figure tO the right shows a PV diagram for a P reversible quasistatic two leg gas compression process The gas starts out at point PiV First leg The gas is first heated at constant volume so that the pressure Al ath A is increased from some P tO some higher value P f Call this intermediate point PfV Second leg The gas is then compressed at constant pressure Pf tO a pi V1 final volume Vf The final state is at PfVf For which leg does heat ow mi the gas Page 10 PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB4 The figure to the right shows a PV diagram for a reversible quasistatic two leg gas compression process There are n moles of gas Take the specific heat of the gas as c in ImolK or L atmmolK The gas constant is denoted as R in JmolK or L atmmolK The gas starts out at point PiV First leg The gas is first heated at constant volume V so that the pressure is increased from some P to some higher value Pf Call this intermediate point PfV Second leg The Pf Vr Al ath A gas is then compressed at constant pressure Pf to a final volume Vf The final state is at Pf Vf What is the total change in the internal energy AEim of the gas TB4 The figure to the right shows a PV diagram for a reversible quasistatic isothermal gas expansion process There are n two moles ofgas Take the specific heat 0fthe gas as c in JmolK or LatmmolK The gas constant is denoted as R in JmolK or L atmmolK The gas starts out at point PiV and ends up at point PfV In terms of the parameters given if needed what is the total change in the internal energy AEim of the gas TB4 The figure to the right shows a PV diagram for a reversible quasistatic isothermal gas expansion process There are n moles ofgas The gas constant is denoted as R in JmolK or L atmmolK The gas starts out at point PiV and ends up at point PfV In terms of the parameters given if needed what is total work done on the gas Won gas during this compression Page 11 PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB4 The figure tO the right shows a PV diagram for a reversible quasistatic isothermal gas expansion process There are n moles Ofgas The gas constant is denoted as R in JmOlK or L atmmOlK The gas starts out at point PiV and ends up at point PfV In terms Of the parameters given if needed what is tOtal heat absorbed by the gas Qin during this compression TB4 The figure tO the right shows a PV diagram for a reversible 1 quasistatic gas cycle The cycle goes 1 AaBaCaDaA The AgtB andthe CgtD legs are adiabatic legs As evident from the diagram the B gt C and D gt A legs are at constant volume For which Of the four legs does heat ow intO the gas 13 TB4 The figure tO the right shows a PV diagram for a reversible quasistatic gas cycle The cycle goes AaBaCaDaA The AgtB andthe CgtD legs are isothermal at temperatures T hm and T cold respectively As evident from the diagram the B gt C and D gt A legs are at constant volume We will take the volumes for DA and BC as at Vhigh and Vlow respectively There are n mOles Of gas The gas constant is denoted as R in JmOlK or L atmmOlK For which Of the four legs does the internal energy Of the gas Eim increase Page 12 PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB4 The gure to the right shows a PV diagram for a reversible quasistatic gas cycle The cycle goes CgtD aA The AgtB andthe CgtD legs are isothermal at temperatures T hot and T cold respectively As evident from the diagram the B gt C and D gtA legs are at constant volume For which of the four legs is positive work done by the gas on the outside world TB4 The gure to the right shows aPV diagram for a reversible quasistatic gas cycle The cycle goes CgtD aA The AgtB andthe CgtD legs are isothermal at temperatures T hot and T cold respectively As evident from the diagram the B gt C and D gtA legs are at constant volume We will take the volumes for DA and BC as at Vhigh and Vlow respectively There are n moles of gas The gas constant is denoted as R in Jmol K or L atmmol K In terms of the parameters given as needed what is the total work done by the gas on the outside world for one complete cycle n The PV diagram in the gure is for an ideal monatornic gas The gas is initially at point A The paths AD and BC represent isothermal changes If the system is brought to point C the change in the internal energy of the gas is 200 V L Page 13 PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET The PV diagram in the gure is for an ideal monatornic gas The gas is initially at point A The paths AD and BC represent isothermal changes If the system is brought to point C the work done by the gas is TB4 200 V L The PV diagram in the gure is for an ideal monatornic gas The gas is initially at point A The paths AD and BC resent isothermal changes R is the versal gas constant Let the pressures volumes and temperatures at the labeled points be denoted as PA PB etc and VA VB etc and TA TB etc respectively CV and C p denote the speci c heats in J or Latm per K at rep uni constant volume or constant pressure 41 200 V L respectively The numbers on the axes of the graph are not relevant to this problem If the system is brought to point C along the path AgtEgtC which expression gives the work done by the gas on the external world Page 14 PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET The PV diagram in the gure is for an ideal monatornic gas The gas is initially at point A The paths AD and BC represent isothermal changes Let the temperatures at the labeledpoints be denoted as T A T 3 etc respectively C V and C p denote the speci c heats in J or Latm per Kin J at constant volume or constant pressure respectively The numbers on the axes of the graph are not relevant to this problem If the system is brought to point C along the path AgtEgtC What is the change in the internal energy of the gas TB4 The PV diagram in the gure is for n moles of anideal monatornic gas The gas is initially at point A The paths AD and BC represent isothermal changes R is the universal gas constant Let the temperatures at the labeled points be denoted as T A T B etc respectively The numbers on the axes of the graph are not relevant to this problem If the system is brought to point C along the path AgtEgtC What is the change in the internal energy of the gas 200 V L 200 V L Page 15 PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB4 The PV diagram in the gure is for n moles of an ideal monatornic gas The gas is initially at point A The paths AD and BC represent isothermal changes R is the universal gas constant Let the pressures volumes and temperatures at the labeled points be denoted as PA PB etc and VA VB etc and TA TB etc respectively If the system is brought to point C along the path AgtEgtC What is the heat absorbed by the gas 200 V L TB4 The PV diagram in the gure is for an ideal monatornic gas The gas is initially at point C The paths DA and CB represent isothermal changes If the system is brought to point A the change in the intemal energy of the gas is 200 V L TB4 The PV diagram in the gure is for an ideal monatornic gas The gas is initially at point C The paths DA and CB represent isothermal changes If the system is brought to point A the work done on the gas is 200 V L Page 16 PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB4 The PV diagram in the gure is for n moles of an ideal monatornic gas The gas is initially at point A The paths AD and BC represent isothermal changes R is the universal gas constant Let the pressures volumes and temperatures at the labeled points be denoted as PA PB etc and VA VB etc and TA TB etc respectively The numbers on the axes of the graph are not relevant to this problem If the system is brought to point C along the path AgtBgtC 200 V L What is the work done by the gas ThePVdiagram in the gure is for an ideal monatornic gas The gas is initially at point A The paths AD and BC represent isothermal changes Let the temperatures at the labeledpoints be denoted as T A T 3 etc CV and C p denote the speci c heats in J or L atm per Kin J at constant volume or constant pressure respectively If the system is brought to point C along the path AgtBgtC What is the change in the internal energy of the gas 200 V L TB4 The PV diagram in the gure is for n moles of an ideal monatornic gas The gas is initially at point A The paths AD and BC represent w changes R is the universal gas constant Let the temperatures at the labeled points be denoted as T A T B etc The numbers on the axes of the graph are not relevant to this problem If the system is brought to point C along the path AgtBgtC What is the change in the internal energy of the gas 100 V L Page 17 PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB4 The PV diagram in the gure is for n moles of an ideal monatornic gas The gas is initially at point A The paths AD and BC represent isothermal changes R is the universal gas constant Let the pressures and the volumes at the labeled points be denoted as PA PB etc and VA VB etc respectively Let the temperatures at the labeled points be denoted as T A T 3 etc The numbers on the axes of the graph are not relevant to this problem If the system is brought to point C along the path AgtBgtC What is the heat absorbed by the gas TB4 The PV diagram in the gure is for n moles of an ideal monatornic gas The gas is initially at point A The paths AD and BC represent isothermal changes R is the universal gas constant Let the temperatures at the labeled points be denoted as T A T B etc Let the pressures and the volumes at the labeled points be denoted as PA PB etc and VA VB etc respectively The numbers on the axes of the graph are not relevant to this problem If the system is brought to point C along the path AgtDgtC 200 V L 401 200 V L What is the work done by the gas on the external world Page 18 PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB4 The PV diagram in the gure is for n moles of an ideal monatornic gas The gas is initially at point A The paths AD and BC represent isothermal changes R is the universal gas constant Let the temperatures at the labeled points be denoted as T A T B etc Let the pressures and the volumes at the labeled points be denoted as PA PB etc and VA VB etc respectively The numbers on the axes of the graph are not relevant to this problem If the system is 200 V L brought to point C along the path AgtDgtC What is the change in the internal energy of the gas TB4 The PV diagram in the gure is for n moles of an ideal monatornic gas The gas is initially at point A The paths AD and BC represent isothermal changes R is the universal gas constant Let the temperatures at the labeled points be denoted as T A T B etc The numbers on the axes of the graph are not relevant to this problem If the system is brought to point C along the path AgtDgtC What is the change in the internal energy of the gas 201 V L Page 19 PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET The PV diagram in the gure is for n moles of an ideal monatomic gas The gas is initially at point A The paths AD and BC represent isothermal changes R is the universal gas constant Let the temperatures at the labeled points be denoted as TA TB etc Let the pressures and the volumes at the labeled points be denoted as PA PE etc and VA VB etc respectively The numbers on the axes of the graph are not relevant to this problem If the system is brought to point C along the path AgtDgtC What is the heat absorbedby the gas The PV diagram in the gure is for an ideal monatomic gas The gas is initially at point A The paths AD and BC represent adiabatic processes Let the temperatures at the labeled points be denoted as TA TB etc Let the pressures and the volumes at the labeled points be denoted as PA PB etc and VA VB etc respectively The numbers on the axes o the graph are not relevant to this problem If the system is brought to point C along the path AgtBgtC What is the work done by the gas 40 200 V L 4iU 200 V L Page 20 PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET The PV diagram in the gure is for an ideal monatomic gas The gas is initially at point A The paths AD and BC represent adiabatic processes Let the temperatures at the labeledpoints be denoted as T A T 3 etc CV and C p denote the speci c heats in J or L atm per Kin J at constant volume or constant pressure respectively Let the pressures and the volumes at the labeled points be denoted as PA PB etc and VA VB etcrespectively The 200 V L numbers on the axes of the graph are not relevant to this problem If the system is brought to point C along the path AgtBgtC What is the heat absorbed by the gas TB4 The PV diagram in the gure is for n moles of an ideal monatomic gas The gas is initially at point A The paths AD and BC represent adiabatic processes R is the universal gas constant Let the temperatures at the labeled points be denoted as T A T B etc Let the pressures and the volumes at the labeled points be denoted as P A P B etc and VA VB etc respectively The numbers on the axes of the graph are not relevant to this problem If the system is 200 V L brought to point C along the path AgtBgtC What is the heat absorbed by the gas Page 21 PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB4 The PV diagram in the gure is for n moles of an ideal monatornic gas The gas is initially at point A The paths AD and BC represent m processes R is the universal gas constant Let the temperatures at the labeled points be denoted as T A T B etc The numbers on the axes of the graph are not relevant to this problem If the system is brought to point C along the path AgtBgtC what is the change in the internal energy of the gas TB4 When an ideal gas undergoes a temperature change at constant volume its internal energy change is given by MW CVAT However this equation also correctly gives the change in internal energy whether the volume remains constant or not Which statement below explains why this is so TB4 When an ideal gas undergoes a temperature change at constant volume the heat input is connected to the change in temperature through Qin C VAT where C V is the speci c heat at constant pressure When the temperature change occurs at constant pressure one has Qin CPAT where CP CV nR is the speci c heat at constant pressure What is the origin of the extra quotnR term when one goes from a constant volume to a constant pressure process TB4 When an ideal gas undergoes an isothermal expansion the pressure volume connection P nRT V follows directly from the perfect gas law Whenwe expand a gas adiabatically we constant 7 obtain a very different looking result namely P where y Cp CV 1 nR CV is always greater than unity This means that the pressure falls off more rapidly with increasing volume for an adiabatic expansion than for an isothermal expansion What is the physical reason for this more rapid fall o Page 22 PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THrs EXAM BOOKLET WITH YOUR ANSWER SHEET TB4 During an isothermal expansion of anideal gas the pressure starts out at some pressure P0 and volume V0 As the expansion proceeds the pressure drops by a factor of two to P0 2 and the volume doubles to 2V0 The gas is then compressed adiabatically from this PV P0 2 2 point back to its original volume V0 but the pressure is now equal to f P0 where f is some number that is greater than 1 What is the correct connection between f and the thermodynamic parameter y C 13 CV where C P and CV are the speci c heats at constant pressure and volume respectively TB4 The gure to the right shows a PV diagram for a standard Carnot gas cycle reversible quasistatic The cycle goes 1 gt 2 isothermal at temperature Th hotbath 2 gt 3 adiabatic from Th down to T cold bath 3 gt 4 isothermal at temperature T 5 and nally for one cycle 4 gtl adiabatic from T5 back to Th For which leg is the change in internal energy AEim positive mlmmmi mpmmn n rquot Allmhdhc cvpmbiun Ad iabauc umprrmnn The gure to the right shows a PV diagram for a standard Carnot gas cycle reversible quasistatic The cycle goes 1 gt 2 isothermal at temperature Th hotbath 2 gt 3 adiabatic from Th down to T5 cold bath 3 gt 4 isothermal at temperature T5 and nally for one cycle 4 gtl adiabatic from T back to Th For which leg is the change in internal energy AEim negative IputhLmml m expansion at rquot Q mummy mpnnsmn Adiabmir cnml mswm l Isothermal Cmnpn ssion ow m 1 r Page 23 PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB4 The gure to the right shows a PV diagram for a standard Carnot gas cycle reversible quasistatic The cycle goes 1 gt 2 isothermal at temperature Th hot bath 2 gt 3 adiabatic from Th down to T5 cold bath 3gt 4 isothermal at temperature T 5 and nally for one cycle 4gt1 adiabatic from T5 back to Th Which legs contribute to the work done either by the gas or on the gas The gure to the right shows a PV diagram for a standard Carnot gas cycle reversible quasistatic The cycle goes 1 gt 2 isothermal at temperature Th hotbath 2 gt 3 adiabatic from Th down to T5 cold bath 3 gt 4 isothermal at temperature T5 and nally for one cycle 4 gt1 adiabatic from T 5 back to T h The gure shows heat going into the gas on isothermal leg 1 gt 2 and out of the gas for isothermal leg 3 gt 4 and no heat in or out for the 2 gt 3 and 4 gt1 adiabatic legs How is this no heat ow in or out for these adiabatic legs accomplished TB4 The gure to the right shows a PV diagram for a standard Carnot gas cycle reversible quasistatic The cycle goes 1 gt 2 isothermal at temperature Th hot bath 2 gt 3 adiabatic from Th down to T cold bath 3 gt 4 isothermal at temperature T 5 and nally for one cycle 4gt1 adiabatic from T 5 back to T h The gure shows correctly that heat Qm ows into the gas from the hot bath for leg 1 gt 2 and heat QM ows out Ofthe gas into the cold bath for leg 3 gt 4 Take the total work by the gas for the cycle as W173 In terms of these parameters if needed what is the total change in the internal energy of the gas AEi g al as one goes around one complete cycle Page 24 toutmar gm rxpanxrrm at T Admlmlir mpmwsron Ad iabnlir commmun 4 Isnllmrmni onmn ssion QMquot Al 1 v Isulhcrmnl Q expansion ar r quot Adiahalir Athabale mmpmum manna 4 Isnllmmml mm ullmmmi Q m r xpumirm a r 139 quot Adialutk Ad mimic 7 n nmpnSsvmv KPansrun 1 limhzrmni mnumsmu Q m a PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB4 For a Carnot refrigerator the cycle shown in gure to the right is run backwards so that the Qm shown owing into the gas from the hot bath for leg lgt 2 now becomes a nglf i owing into the hot bath for a 2 gtl leg the QW shown owing out of the gas into the cold bath for leg 3 gt 4 becomes a erf lg owing into the gas from the cold bath and the previous total work done by the Carnot engine W173 now becomes the total work done on the gas Wgt mz from an external power source erj 1g Q53 and W3 are positive quantities Which of the following refrigerator parameter connections is valid Hint It is sugges label parameters on the diagram to help your reasoning For a Carnot refrigerator the cycle shown in gure to the right is run backwards so that the Qm shown owing into the gas from the hot bath for leg 1 gt 2 now becomes a Q33 owing into the hot bath for a 2 gtl leg the Q0 shown owing out of the gas into the cold bath for leg 3 gt 4 becomes a erj g owing into the gas from the cold bath and the previous total work done by the Carnot engine W173 now becomes the total work done on the gas Wgt mz from an external power source erj 1g Q53 Isulhcrmnl k expansion m Adiabalir Axlmbavhz cmupmum manna ltl ted that you redraw arrows and re lsullmmml n Mammy m rquot mbm Admbnhr N expansion mmpmmm 4 lmlharmal men asirm M 1 and mm are positive quantities The Coef cient of Performance or COP r a refrigerator is de ned as the ratio of the heat extracted from the cold bath divided by the total work input to the system Which of the equations below express this result Page 25 PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB4 The quasistatic ideal gas cycle shown to the right has three legs anadiabatic leg 1 from P2V1 to P 1 atmV3 followed by an isobaric compression leg 2 from P 1 atmV3 to P 1 atmV1 and ending with a constant volume pressurization leg 3 from P 1 atmV1 back to the initial state to complete the cycle There are n moles of gas What happens to the internal energy Em during leg 2 of this process Hint Label the legs 1 2 and 3 in the diagram for more clarity TB4 The quasistatic gas cycle for n moles of an ideal monatomic gas as shown to the right has three legs an adiabatic leg 1 from P2V1 to P 1 atmV3 followed by anisobaric compression leg 2 from P 1 atmV3 to P 1 atmV1 and ending with a constant volume pressurization leg 3 from P 1 atmV1 back to the initial state to complete the cycle What happens to the internal energy Em during leg 1 of this process Hint Label the legs 1 2 and 3 in the diagram for more clarity TB4 The quasistatic gas cycle for n moles of anideal monatomic gas as shownto the right has three legs an adiabatic leg 1 from P2V1 to P 1 atmV3 followed by anisobaric compression leg 2 from P 1 atmV3 to P 1 atmV1 and ending with a constant volume pressurization leg 3 from P 1 atmV1 back to the initial state to complete the cycle What happens to the internal energy Em during leg 3 of this process Hint Label the legs 1 2 and 3 in the diagram for more clarity Page 26 hum 1 Adinbatic I Hahn 1 2 Adidbntic 1 v V VL Patm Iquot Adinbatic l V v I39L PH141 Fall 2011 Test Bank 4 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB4 The quasistatic gas cycle for n moles of anideal monatomic gas as shownto the right has three legs an adiabatic leg 1 from P2V1 to P 1 atmV3 followed byanisobaric compression leg 2 from P 1 atmV3 to P 1 atmV1 and ending With a constant volume pressurization leg 3 from P 1 atmV1 back to the initial state P2V1 to complete the cycle What is the change in the internal energy Eim during leg 3 ofthis process Hth 1 Label the legs 1 2 and 3 in the diagram for more clarity TB4 The quasistatic gas cycle for n moles of an ideal monatomic gas as shown to the right has three legs an adiabatic leg 1 from P2V1 to P 1 atmV3 followed by anisobaric compression leg 2 from P 1 atmV3 to P 1 atmV1 and ending With a constant volume pressurization leg 3 from P 1 atmV1 back to the initial state to complete the cycle Is the heat ow into the gas Qm positive heat ows in negative heat ows out or zero for leg 2 of this process Hint 1 Label the legs 1 2 and 3 in the diagram for more Ad 1 a batic Ad idbntiC v v v L clarity Hint 2 The molar heat capacity for a monatomic ideal gas is given by cquot R and the ideal gas law is PV nRT Page 27 PH141 Fall 2011 Test Bank 3 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET Student 1 legible Name legible Section 01 or 02 1 A Fill in your student number last name and initials on the bubble sheet Do these clearly and carefully Errors will result in a rejected bubble sheet B Mark your exam version A or B C Hand write in your section number 001 or 002 in the section block on the bubble sheet D Fill in your name and section number on the exam booklet 2 While the exam is open book and open notes gno calculators or eletronic devices of any kind 1 you would be prudent to keep the use of these open book materials to a minimum These are concept questions that involve basic understanding and a few key equations There is essentially very little that you can look up from your book or notes There are essentially no quotequations to fmd quot You should have the basic concept equations in your head 3 It is recommended that you work in this booklet and wait until 10 20 minutes before the end of the period to mark your answer sheet Mark up the booklet any way you like It is recommended that you not waste time erasing This is a workbook 4 Make sure to use a soft 2 pencil to fill in the ovals on the bubble sheet Note that erasures 011 the bubble sheet can result in misreads and machine grading errors Please make sure of your answer before marking the bubble sheet 5 Ten minutes before the end of the period you will be reminded to begin to wrap things up and mark answers on your bubble sheet 6 Five minutes before the end of the period you will be reminded to wrap things up and turn in your booklet and answer sheet 7 The exam has 12 questions Each question is worth 9 points The maximum score is 108 It is the raw score that counts So you get a quotspotquot of 8 points A perfect score will net you 108 points toward the in terrn exam average Eg you can miss 2 problems and still get an A miss 3 and still get B etc Addendum on academic integrity the academic integrity policy for this course is stated brie y in the syllabus and in detail in the separate document posted on RamCT Failure to abide by these rules will be considered academic dishonesty and will be dealt with according to university policy For exams exams are to be your own work and no consultation with other persons directly or indirectly is allowed You are not allowed to use any materials unless speci cally authorized to do by course policy or by the instructor It is never acceptable to copy work from another student Page 1 PH141 Fall 2011 Test Bank 3 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET Possibly useful physics equations and connections Wherever needed take the gravitational acceleration parameter g as equal to 10 msz Derivative connections between 1D position xt velocity vxt and acceleration ax t axt vxt vx t xt Use slopes instead of derivatives whenever possible Integral connections between 1D position xt velocity vxt and acceleration ax t a sz v M1 Avxt j axtdt Axt j vxtdt ammo mea Use areas instead of integration whenever possible Centripetal acceleration ac and centripetal force F 5 both inward for a point mass m going mv2 R Newton s First Law An object in motion constant velocity tends to stay in motion same velocity 2 around a circle ofradius R with a speed v a Fc Newton s Second Law F ma m md 2x dt d Newton s Third Law For every force applied toin a system there is an equal and opposite force action reaction Hooke s law spring force law F kx end Xena Work force acting over a distance W I F d 7quot in 1D I dex Favg gtlt distance start Xmm Kinetic energy K mv2 Gravity work ngv mgh Spring work Wsprmg kx2 equot a 1 1 Work 7 k1net1c energy theorem work on a free mass I F d r Emvgnd Emvsztm start Maximum static friction force F5123 motion uan stationary mass Kinetic friction force Fkine c motion uan moving mass dzx dvdmvdp Momentum de ned from quotF maquot F m m p mv d dt dt dt d quotF maquot and actlonreact1on bas1s for momentum conservatlon 1 F 7p 3 dp Fair 1 means that a force Fl acting over an incremental time dt on an object 1 causes a change in momentum dp for object 1 2 Action reaction says that the object 2 providing this force suffers an equal and opposite force namely F 2 F1 and this force is applied for the same dt We have therefore dpg dp1 Page 2 PH141 Fall 2011 Test Bank 3 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET Elastic collisions momentum and kinetic energy are conserved in 1D the speed of approach for the oncoming masses in atwo mass collision equals the speed separation after the collision Inelastic collisions momentum is conserved but energy is not conserved Rotational dynamics based on TM and standard notation S Rt9 dSdt v Rdt9dtRa aIZSalt2 Ralzt9ah 2 Rda2dtRa Torque for forces perpendicular to the lever arm pivot line etc 139 RF I a rotational analog to F ma Moment of inertia Mass on the end ofa massless rod I MR2 Rimmed wheel all mass uniformly distributed around circumference I MR2 Rod of length L and mass M rotating about an axis at one end and perpendicular to the rod I l 3ML2 Uniform disk of radius R and mass M rotating about an axis through the center and perpendicular to the disk I l 2MR 2 Torque and angular momentum vector connections 3 17 X F I0 dEdt E 7 X 27 IE The vector cross product gtlt 6A3 direction of 21 X R by right hand rule Universal gravitation force law F12 Gmlmg r122 attractive 7 this is a concept equation Gravitational potential energy U r of a point mass m in the gravitational eld of a uniform spherical shaped object of mass M at a distance r away from the center and with U taken as zero at roo Ur GMmr Effective gvalue at the surface of a planet g GM R2 Energy balance for the escape velocity vm of a mass m launched from the surface of a uniform 1 GM spher1cal planet of mass M and rad1us R Emvgsc m Solid angle rules for hollow or variable density spheres with spherical symmetry All mass elements outside the radius r of the observer yield a net g value of zero How do F ma and Hooke s Law F kx combine to give harmonic motion that is with x x0 sina0t mo Vkm etc Frequency and period connections m0 27239f0 f0 lTo f0 mg 27239 etc do you see the connections Harmonic motion connections x x0 sin mot vx xowo cos mot ax x0ag sin mot etc Harmonic motion and phase How can xt x0 cosa0t 5 xt x0 sina0t and xt xc cosa0t xs sin mot all be equivalent How do 139 I a and the restoring force dynamics for a pendulum made of a light string of length L and a mass m combined with the small angle approximation sin 9 m 9 yield small angle harmonic motion 9 60 sin mot mo g L etc How does pendulum motion in accelerated reference frames work For linear accelerated motion For circular motion For accelerated motion down an incline Answer If there is an 5 the accelerated system feels an effective gravity ge 5 in addition to any regular g that might be present Page 3 PH141 Fall 2011 Test Bank 3 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET sin sin Transverse harmonic wave yxt A cos kx wt or cos 27r 27r etc etc Velocity for a wave v if mk d 2 t 1 d2 1 Transverse wave equatlon x v2 dt2 v d fmeaw si m fsource statlonary recelver Vsound H Source Vsound i receiver fieceiver fsome Statlonary source Vsound Perfect gas law PV nRT NkBT gmng temperature kinetic energy Absolute zero temperature To 0 K m 27315 C Possibly useful math connections Sin 2 oppos1te 08 2 adjacent nan oppos1te hypotenuse hypotenuse ad acent sin30 1 2 cos30 52 sin 30 cos 60 sin 60 cos 30 rule for complimentary angles sin45 J 21JE cos45 J 21J tant9 singcos sin2t9cos2t9 1 2sin 9 cos 9 sin 26 sin A B sin A cos B cos A sin B get sinA B from symmetry sin 61 sin 62 2cost91 62 sin 091 62 d 71 Der1vat1ve connectlon for xquot d xquot nxquot x Circumference of a circle C 2727 Area ofa circle A In2 Area ofa sphere A 47239quot2 Volume of a sphere V 37273 Page 4 PH141 Fall 2011 Test Bank 3 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBS The gure to the right shows a mobile with four Objects on three rods The rods have negligible mass Take the tensions in the cords hanging from the lowest bar as T512 and T Llngm le and right ends respectively the tensions in the cords from the middle bar as TMllg and TMlngm those for the umbar as TUnZ and Tylngm and the tension in the cord from the bracket as T BR Which Of the following equations are consistent with force and torque balance TBS The gure to the right shows a mobile with four Objects on three rods The rods have negligible mass Take the tensions in the cords hanging from the lowest bar as T512 and T Llngm le and right ends respectively the tensions in the cords from the w bar as TMllg and TMlngm those for the umbar as TUnZ and Tylngm and the tension in the cord from the bracket as T BR Which Of the following equations are consistent with force and torque balance TBS The gure to the right shows a mobile with four Objects on three rods The rods have negligible mass Take the tensions in the cords hanging from the lowest bar as T512 and T Llngm le and right ends respectively the tensions in the cords from the middle bar as TMllg and TMlngm those for the umbar as TUnZ and Tylngm and the tension in the cord from the bracket as T BR Which Of the following equations are consistent with force and torque balance Page 5 PH141 Fall 2011 Test Bank 3 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBS A 4 m long horizontal construction beam of mass M is supported against a brick wall by a strong light weight which you may take as massless cable extending from the wall down to the right end of the beam as shown The le end of the beam is held up by friction only How high above the beam does the cable meet the wall TBS A 4 m long horizontal construction beam of mass M is supported against a brick wall by a strong light weight which you may take as massless cable extending from the wall down to the right end of the beam as shown Take the cable tension as T the friction force Onthe beam from the wall as F fm and the normal force on the beam from the wall and from the beam on the wall as F all taken as positive quantities Take the angle between the beam and the cable as 8 Which equation below states correctly the horizontal force balance TBS A 4 m long horizontal construction beam of mass M is supported against a brick wall by a strong light weight which you may take as massless cable extending from the wall down to the right end of the beam as shown Take the cable tension as T the friction force Onthe beam from the wall as F fm and the normal force on the beam from the wall and from the beam on the wall as F all taken as positive quantities Take the angle between the beam and the cable as 8 Which equation below states correctly the vertical force balance TBS A 4 m long horizontal construction beam of mass M is supported against a brick wall by a strong massless cable that extends from the wall down to the right end of the beam as shown Take the cable tension as T the friction force on the beam from the wall as F fm the normal force on the beam from the wall and from the beam on the wall as F and the angle between the beam and the Page 6 PH141 Fall 2011 Test Bank 3 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET cable as 8 Which equation below states correctly the torque balance Hint Replace the 4 m length of the beam by a length parameter L or take each side of the equations below to contain a l m multiplier to keep the dimensions correct for your torque analysis TB3 A 4 m long horizontal construction beam of mass M is supported against a brick wall by a strong light weight which you may take as massless cable extending from the wall down to the right end of the beam as shown Take the cable tension as T the friction force on the beam from the wall as Ff and the normal force on the beam from the wall and from the beam on the wall as F One possible torque balance equation is Ffm T sin 8 Where is the rotation axis for this particular form TB3 A ladder ofmass M shown as 20 kg in the gure and length L leans against a well and is tethered to the wall with a wire at the bottom as shown There are four forces on the ladder the normal force upward from the oor RF10m onthe bottom of the ladder the tension force from the wire T WW also at the bottom of the ladder and to the right the downward Mg force taken to be applied at the center of mass of the ladder and the normal force from the wall F quot4mg pushing to the le at the very top of the ladder Take the angle between the wire and the ladder as 8 Which of the following force balance equations is correct Hint39 label in the ladder length forces and angles and work from your diagram m m Him TB3 A ladder ofmass M shown as 20 kg in the gure and length L leans against a well and is tethered to the wall with a wire at the bottom as shown There are four forces on the ladder the normal force upward from the oor F n aw on the bottom of the ladder the tension force from the wire T WW also at the bottom of the ladder and to the right the downward Mg force taken to be applied at the center of mass of the ladder and the normal force from the wall F quot4mg pushing to the le at the very top of the ladder Take the angle between the wire and the ladder as 8 Which of the following force balance equations is correct Hint39 label inthe ladder length forces and angles and work from your diagram m m Page 7 PH141 Fall 2011 Test Bank 3 Test version X mark this version on your answer sheet YOU MUST RETURN THrs EXAM BOOKLET WITH YOUR ANSWER SHEET TBS Aladder Ofmass M shown as 20 kg in the gure and length L leans against a well and is tethered to the wall with a wire at the bottom as shown There are four forces on the ladder the normal force upward from the oor Fm10m on the bottom Of the ladder the tension force from the wire T WW also at the bottom Of the ladder and to the right the downward Mg force taken to be applied at the center Of mass Of the ladder and the normal force from the wall F lm pushing to the le at the very top Of the ladder Take the angle between the wire and the ladder as 8 For a rotation axis at the mm gt top Of the ladder which Of the following torque balance equations is correct Hint label in the ladder length forces and angles and work from your diagram TBS A ladder Ofmass M shown as 20 kg in the gure and length L leans against a well and is tethered to the wall with a wire at the bottom as shown There are four forces on the ladder the normal force upward from the oor F n aw Onthe bottom Of the ladder the tension force from the wire T WW also at the bottom Of the ladder m m and to the right the downward Mg force taken to be applied at the center Of mass Of the ladder and the normal force from the wall F quot4mg pushing to the le at the very top Of the ladder Take the angle between the wire and the ladder as 8 For a rotation axis at the bottom Of the ladder which Of the following torque balance equations is correct Hint39 label in the ladder length forces and angles and work from your diagram TBS Consider two planets the earth with a mass ME and radius RE and a very large planet with a mass M P and a radius R P Assume that the two planets have the same densities that is the density p 3M 47rR3 is the same for both planets What is the ratio Of the escape velocities VP vE for a small mass launched from the surfaces Of the two planets P and E respectively Hint Express the masses in terms Of the densities and the radii and thenwork out the escape velocities from energy conservation TBS Consider two planets the earth with a mass M E and radius R E and a very large planet with a mass MP and a radius RP gtgt RE Assume that the two planets have the same masses that is we have ME MP What is the ratio Ofthe escape velocities vPvE for a small mass launched from the surfaces Of the two planets P and E respectively Page 8 PH141 Fall 2011 Test Bank 3 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB3 Take the radii of the earth and the moon as R E and RM and their surface gvalues as g E and g M respectively Which of the expressions below expresses correctly the ratio of their average densities namely p E p M Hint express the surface gvalues in terms of G the universal gravitational constant M and R Then express eachM in terms of the density p and R of the body Take ratios and solve for 5 pM TB3 Take the radii ofthe earth and the moon as RE and RM and their masses as ME and MM respectively Which of the expressions below expresses correctly the ratio of their average densities namely 3 pM TB3 Take the radii of the earth and the moon as RE and RM and their masses as ME and MM respectively Which of the expressions below gives the ratio of their surface escape speeds TB3 Take the radii of the earth and the moon as RE and RM and their masses as ME and MM respectively For zero potential energy U taken at r 00 what is the approximate ratio of the potential energies for a test mass m0 at the surfaces of the earth and the moon respectively e g UEREUMRM TB3 An object initially at rest is dropped from a height h above the surface of Earth If the height h equals to the radius of the Earth RE and there is no air resistance what is the speed of the object v when it strikes the Earth TB3 An object of mass m initially at rest is dropped from a height h above the surface of Earth If the height h is twice the radius of the Earth RE and there is no air resistance what is the kinetic energy K of the object when it strikes the Earth TB3 An object of mass m initially at rest is dropped from rest from a height h above the surface of Earth Ifthe height h is twice the radius of the Earth RE and there is no air resistance what is the ratio of the object s kinetic energy K to the potential energy U when the object strikes the Earth Page 9 PH141 Fall 2011 Test Bank 3 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB3 A point particle of mass m is positioned on the x axis at x L and an identical point particle is positioned on the y axis at y L What is the vector gravitational eld g at the origin TB3 A point particle of mass m is on the x axis at x L and an identical point particle is on the y axis at y L What is the magnitude of the gravitational eld g at the origin TB3 A point particle of mass m is on the x axis at x 2L and an identical point particle is on the y axis at y L What is the vector gravitational eld g at the origin TB3 A nonuniform thin rod of length L lies on the x axis One end of the rod is at origin and the other end is at x L The rod s mass per unit length it varies as l Cx where C is a constant What is the gravitational eld due to the rod on the x axis at x 2L TB3 A straight smooth tunnel is dug through a uniform spherical planet of mass density p0 The tunnel passes through the center of the planet and is perpendicular to the planet s axis of rotation which is xed in space The planet rotates with a constant angular speed a so objects in the tunnel have no apparent weight Consider a particle of mass m which is in the tunnel and is at a distance of r away from the center of the planet What is the kinetic energy of this particle TB3 Athick spherical shell of mass M and uniform density has an inner radius a and an outer radius 3a What is the gravitational eld at r a 2 Note that r is the distance from the center of the spherical shell TB3 A thick spherical shell of mass M and uniform density has an inner radius a and an outer radius 3a What is the gravitational eld at r 2a Note that r is the distance from the center of the spherical shell Page 10 PH141 Fall 2011 Test Bank 3 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET Four identical planets each ofmass M are arranged in a square of side length a The assembly is in a circular orbit around their common center as shown in the gure What is the centripetal force on each planet toward their common center Hint 1 sm 45 cos 45 J5 Four identical planets each ofmass M are arranged in a square of side length a The assembly is in a circular orbit around their common center as shown in the gure Assume that we have calculated the inward force toward the center for each mass as GM 2 FGC a2 where C is an appropriate numerical constant For an orbital speed v0 for each planet which of the equations below express correctly the proper force balance what the force has to be and where it comes from Hint sin 45 cos 45 J5 Orb TB3 Consider the calculation of the gravitational eld at some point P located at a distance xP out along the x7 axis from the center ofathin rod ofmass M and length L that is also along the x7 axis and centered 0 See gure Which expression below gives the contribution dg to the gravitational eld at point P from the mass element dm at position xs TBS Consider the calculation of the gravitational potential energy of a test mass m0 not shown at some point P located at a distance xP out along the x axis from the center ofa thin rod ofmass M and length L that is also along the x axis and centered at x 0 See gure The mass ofthe rod is uniform Which expression below gives the contribution dU to the potential energy of the test mass m0 at point P from the mass element dm at position XS Page 11 PH141 Fall 2011 Test Bank 3 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB3 A thin uniform rod of mass M is bent into a semicircle with a radius R and positioned in an x y coordinate system as shown Which components of the gravitational eld go at the center ofthe semicircle eg at x y 0 if any is are zero TB3 A thin uniform rod of mass M is bent into a semicircle with a radius R and positioned in an x y coordinate system as shown One wishes to obtain the x component of the gravitational eld go at the center of the semicircle eg at x y 0 Which integral below will give this result TB3 A thin uniform rod of mass M is bent into a semicircle with a radius R and positioned in an x y coordinate system as shown One wishes to obtain the y component of the gravitational field go at the center of the semicircle eg at x y 0 Which integral below will give this result TB3 A thin uniform rod of mass M is bent into a semicircle with a radius R and positioned in an x y coordinate system as shown One wishes to obtain the y component of the gravitational field go at the center of the semicircle eg at x y 0 through the use of the usual integral form goy S 2J39sint9dm What is dm TB3 A pendulum hanging from the ceiling of a cargo van is comprised of a mass on the end of a light string of length L As we have derived when the truck is at rest or traveling at constant speed the angular frequency of the pendulum small angle motion is given by wo l g L What is the Page 12 PH141 Fall 2011 Test Bank 3 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET frequency if the truck is accelerating at a constant rate all Hint Think about effective gravity in accelerating systems TB3 A pendulum hanging from the ceiling of a cargo van is comprised of a mass on the end of a light string of length L As we have derived when the truck is at rest or traveling at constant speed the angular frequency of the pendulum small angle motion is given by m0 m What is the frequency if the truck going around a curve of radius R at a speed v1 is accelerating at a constant rate a1 Hint Think about effective gravity in accelerating systems TB3 A pendulum hanging from the ceiling of a cargo van is comprised of a mass on the end of a light string of length L As we have derived when the truck is at rest or traveling at constant speed the angular frequency of the pendulum small angle motion is given by m0 l g L What is the frequency if the truck going down a incline at an angle 9 to the horizontal at a constant speed v1 TB3 A pendulum hanging from the ceiling of a cargo van is comprised of a mass on the end of a light string of length L As we have derived when the truck is at rest or traveling at constant speed the angular frequency of the pendulum small angle motion is given by m0 l g L What is the frequency if the truck going over the crest of a hill with a radius of curvature R at a speed v1 TB3 A particle undergoes oscillatory motion in 1D with a position function xt x0 sina0t Take mg as 6 rads What is the rst time call it t01 after the t 0 point for which the particle is instantaneously back at x 0 TB3 A particle undergoes oscillatory motion in 1D with a position function xt x0 sina0t Take the period of the oscillation as T0 What is To in terms of the angular frequency m0 TB3 A particle undergoes oscillatory motion in 1D with a position function xt x0 sina0t Take the period of the oscillation as To What is the rst time taken as tvo after t 0 that the speed ofthe particle vxt is the same as at t 0 Page 13 PH141 Fall 2011 Test Bank 3 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBS A particle undergoes oscillatory motion in 1D with a velocity function v1C t v0 sin wot In terms of v0 too and appropriate harmonic trig functions Which of the following is a valid xt position function for this motion The simple harmonic motion Ofa particle in 1D can be Written as xt x0 coswt5 What is the value Ofthe velocity vxt Ofthis particle at time t 0 TBS The simple harmonic motion Ofa particle in 1D can be Written as xt x0 coswt5 What is the value Ofthe acceleration axt Ofthis particle at time t 0 TBS An Object on a frictionless horizontal surface oscillates at the end of a spring With an amplitude OflO cm Its total mechanical energy is 01 J What is the force constant k Ofthe spring TBS An Object on a frictionless horizontal surface oscillates at the end of a spring If the spring has a force constant of 200 Nm and the total mechanical energy is 10 J What is the amplitude An of the oscillation TBS A simple pendulum OflengthL is attached to a massive cart that slides Without friction down a plane inclined at angle 8 With the horizontal as shown in the gure What is the frequency of oscillation for small oscillations of this pendulum TBS A linearly damped oscillator has a Q factor of 60 By What fraction f Azipmyde does the energy decrease during each cycle Page 14 PH141 Fall 2011 Test Bank 3 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET Consider the system shown in the ure vvithtvvos Ii 5 connectedto k k1 aims m inapuihfw TinWW WNWWWL L arrangement The right spring with a spring constant k2 3kg is three times as stiff as the le spring with k1 k0 What is the period of the oscillation T for the mass for this arrangement Hint What is the effective spring constant for this setup in terms of m and k0 TBS cogsit vder the system 511015113111 the gure I I k W1 osnnsconnece oamassm In J a series endmind arrangement The right 4 r MMVWWw vi ME spring with a spring constant k 3kg is three times as stiffas the le spring with k1 k0 What is the period ofthe oscillation T for the mass for this arrangement Hint What is the effective spring constant for this setup in terms of m and k0 TBS coglsit vder the system shorting in the gure I M k2 W1 osnnsconnece oamassm 1n a series endmind arrangement The right 4 Vii ii i lni liVlyl uu Wil ij V JiAiME spring with a spring constant k 3kg is three times as stiff as the le spring with k1 k0 For an oscillation amplitude x0 what is the total mechanical energy E m of the oscillating system Hint What is the effective Spring constant for this setup in terms of m and k0 TBS A spherically symmetric mass or radius R has a density kgm3 that scales inversely with the square of the distance r from the center of the mass and follows pr C r2 Which of the integrals below will yield the mass of the sphere Hint Construct your dm for a spherical shell TBS A spherically symmetric mass or radius R has a density kgm3 that scales inversely with the square of the distance r from the center of the mass and follows pr C r2 What are the units of the constant C Page 15 PH141 Fall 2011 Test Bank 3 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBS A spherically symmetric mass or radius R has a density kgm3 that scales inversely with the distance r from the center of the mass and follows pr C r Which of the integrals below will yield the mass of the sphere Hint Construct your dm for a spherical shell TBS A spherically symmetric mass or radius R has a density kgm3 that scales inversely with the the distance r from the center ofthe mass and follows pr Cr Which ofthe integrals below will yield the gravitational eld at a point r m lt R Inside the sphere Hint Construct your dm for a spherical shell integrate and apply the gravitation law TBS A simple pendulum of length L is attached to a massive cart that slides without friction down an incline at an angle 8 as shown in the gure As we know the acceleration of the cart downthe incline is equal to gsinB Use the concept of effective gravity for an accelerated system to obtain the total effective gravitational acceleration parameter gm as experienced by the pendulum Hint 1 Draw appropriate vectors for the downward acceleration of gravity g and the effective gravity due to the acceleration and add these vectors together Hint 2 Look at obvious limits TBS A simple pendulum of length L is attached to a massive cart that slides without friction down an I incline at an angle 8 as shownin the gure As we know the acceleration of the cart down the incline is U y equal to g sinB From the concept of effective Mi gravity with appropriate vectors for the downward acceleration of gravity g and the effective gravity up the incline geff gsinB one obtains atotal effective gravity gm g cos 8 that points down and to the right in the gure at an angle 8 to the vertical This being the case what will be the angular frequency of the pendulum undergoing small angle oscillations Page 16 PH141 Fall 2011 Test Bank 3 Test version X mark this version on your answer sheet YOU MUST RETURN THrs EXAM BOOKLET WITH YOUR ANSWER SHEET TBS A simple pendulum Of length L is attached to a massive cart that slides without friction down an incline at an angle 8 as shownin the gure As we know the acceleration Of the cart downthe incline is equal to g sinB From the concept Of effective gravity with appropriate vectors for the downward acceleration Of gravity g and the effective gravity up the incline geff gsinB one Obtains atotal effective gravity gm g cos 8 that points down and to the right in the gure at an angle 8 to the vertical If the pendulum is in equilibrium that is not swinging at all which way will it hang as the cart accelerates down the incline TBS A simple pendulum Of length L is attached to a f massive cart that slides without friction down an I 2 incline at an angle 8 as shownin the gure Assume that the acceleration Of the massive cart down the v K r incline adown is unaffected by any pendulum motion What is adown TBS Consider the tunnel through the earth problem shownin the gure At a distance r from the center Of the earth as indicated what is the magnitude Of the gravitational force F g Take the mass density to be constant That is the mass is uniform TunmI Page 17 PH141 Fall 2011 Test Bank 3 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBS Consider the tunnel through the earth problem shown in the gur ake x 0 at the center Ofthe tunnel and positive x to the right as labeled At a general position x which can be positive or negative from the center Of the tunnel what is the Tums correct expression for the x 7 component Of the force 1 Take the mass density to be constant That is the mass is uniform TBS Consider the tunnel through the earth problem shown in the gure For an Observer at position x as shown at a distance r from the center Of the earth what is the value Of the acceleration Of gravity g at this point Take the mass density to be constant That is the mass is uniform Hint This has nothing to do with the tunnel per se TBS Consider the tunnel through the earth problem shownin the gure e x 0 at the center Ofthe tunnel and positive x to the right as labeled At a general position x which can be positive or negative from the center Of the tunnel what is the correct expression for the angle between the force vector 15 and th 39s TBS Consider a uniform rope Of mass M and length L that is suspended from a ceiling and hangs straight down Let the distance from the ceiling to some point on the rope be denoted as x What is the tension T in the rope as a function Of x TBS Consider a uniform rope Of mass M and length L that is suspended from a ceiling and hangs straight down Let the distance from the ceiling to some point on the rope be denoted as x A wave pulse is launched by an excitation transducer at the point Of attachment to the ceiling What will an Observer see as the wave pulse propagates down the rope Page 18 PH141 Fall 2011 Test Bank 3 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB3 Consider a horizontal rope of length L and with a density per unit length x that decreases as one moves from the left end of the rope x 0 to the right end x L according to ux 0 ex with OL lt 0 of course to keep the mass element dm uxdx always positive Which expression below gives correctly the total mass M of the rope TB3 Consider a horizontal rope of length L and with a density per unit length ux that decreases as one moves from the left end of the rope x 0 to the right end x L according to ux 0 ex with OL lt 0 of course to keep the mass element dm uxdx always positive A wave pulse is launched by an excitation transducer at the left end of the rope What will an observer see as the wave pulse propagates to the right toward positive x along the rope TB3 The driver of a car traveling at a speed um toward a vertical wall brie y sounds the horn The horn frequency is fhm When the driver hears the echo from the wall she hears a frequency fm What is fm in terms of fhgm Take the sound wave speed in air as vmnd TB3 The driver of a car traveling toward a vertical wall brie y sounds the horn The sound wave produced by the horn has a frequency fhom When the driver hears the echo from the wall she hears a frequency fheard If the sound wave has a speed vmmd what is the speed of the car 507 TB3 The driver of a car traveling at a speed umy toward a vertical wall brie y sounds the horn The sound wave produced by the horn has a frequency fhom When the driver hears the echo from the wall She hears a frequency f heard What is the speed of the sound vsmd TB3 Which of the following equations describe the propagation of a wave pulse yx t on a string toward negative x Take the speed of the wave v as positive Page 19 PH141 Fall 2011 Test Bank 3 Test version X mark this version on your answer sheet YOU MUST RETURN THrs EXAM BOOKLET WITH YOUR ANSWER SHEET TBS The diagram to the right shows a schematic Of the first ve A standing modes for a pipe that is closed at the left end and Open x at the right end If the length Of the pipe is L and the quot quot N quotquotquot quotm wavelength Ofa given mode with index n n l 23 is denoted as A which Of the following indexing schemes is correct TBS The diagram to the right shows a simpli ed A A schematic Of the third harmonic standing mode N N I for the tube in the human ear For purposes Of i calculation take the length Of the tube closed at Third harmonic the le end and Open at the right end as 3 cm lfthe speed Of sound is 360 ms what is the frequency fn Ofthis mode TBS The diagram to the right shows a simpli ed schematic Of the fundamental rst harmonic N standing mode for the tube in the human ear Note that the tube is closed at the le end and Fundamem 1 39539 WWW u gt Open at the right end If the tube ruptured in some way unfortunately what would happen to the frequency Of the fundamental mode Two traveling waves in 1D have the same frequency the same wavelength and the same amplitude and are traveling inthe same direction The waves are out Ofphase by 180 lfthese waves were added together how would the amplitude change from that Of one Of the initial waves Two traveling transverse waves have the same frequency the same wavelength and the same amplitude and are traveling in the same direction but the waves are out Of phase The yx t response functions for the two waves are given as yl x t Asinloc wt 7 25 and Page 20 PH141 Fall 2011 Test Bank 3 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET yzxt Asinkx wt Ifthese waves are added together what is the amplitude AM ofthe resulting wave y 2 y1xt yzxt TBS Two traveling transverse waves have the same frequency the same wavelength and the same amplitude and are traveling in the same direction but the waves are out of phase The yxt response functions for the two waves are given as yl x t Asinkx wt 7 25 and y2 xt A sinkx wt Ifthese waves are added together what is the angular frequency wHZ Of le resulting wave ym yrxt y2xgtt TBS A transverse traveling wave on a taunt string is described by the standard equation yxt Asin27r7 Z TLi 5 The frequency is 40 Hz Two xed points on the string a distance of 5 m apart oscillate with a phase difference of 30 What is the wavelength A of the wave TBS A transverse traveling wave on a taunt string is described by the standard equation yxt A sin27r7 27 The frequency is 40 Hz Two xed points on the string a distance Ax apart oscillate with a phase difference of 5 What is the wavelength A of the wave S A transverse traveling wave on a taunt string is described by the standard equation yxt A sin27r7 27 where the wavelength Ii and the period T are both known If the oscillations in time are observed for two different positions a distance Ax apart what is the phase 5 difference between these oscillations TBS Two point sound sources are located along a vertical yiaxis at xy 0dU 2 and x y 0751U 2 eg the source separation is equal to dn At a distance D out along the x7 axis constructive interference is detected at the center point the horizontal dashed line in the gure and at a rst interference maximum angle of BB Which of the equations below describes the proper phase lengthangle condition for this rst offaxis maximum Page 21 PH141 Fall 2011 Test Bank 3 Test version X mark this version on your answer sheet YOU MUST RETURN THrs EXAM BOOKLET WITH YOUR ANSWER SHEET TBS Two point sound sources are located along a vertical yiaxis at xy 0dU 2 and x y 0751U 2 eg the source separation is equal to dn At a distance D out along the x 7 axis constructive interference is detected at the center point at 8 Bu 0 along the horizontal dashed line in the gure and at a rst interference maximum angle at 8 81 In between these two maxima there is a null point in the signal at 8 Bu Which Of the equations below describes the proper phase lengthangle condition for this Offaxis null point The wave function for a certain standing wave on a string is given by yxt AU sinknx sinwut where kn 37 radm and on 67 rads What is the wavelength Au Of the standing wave TBS The wave function for a certain standing wave on a string is given by yxt AU sinknx sinwut where kn 37 radm and on 67 rads What is the period TB of the standing wave oscillation in seconds TBS The wave function for a certain standing wave on a string is given by yxt AU sinknx sinwut where kn 37 radm and on 67 rads We also know that a standing wave can be considered as a superposition Of two traveling waves going in Opposite directions with the save wave vector and the same frequency What will be the common speed VD Of the two traveling waves that make up the standing wave given above TBS The temperature is 10 C in Classroom A and is 50 0F in Classroom B Which Of the following is true The temperature is 16 C in Classroom A is 59 0F in Classroom B and is 291 K in Classroom C Which classroom is the coldest one Page 22 PH141 Fall 2011 Test Bank 3 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB3 The temperature 59 F equals to TB3 Liquid nitrogen is much cheaper than liquid helium The molecular weight of diatomic nitrogen N2 is about 28 gmole and that of atomic helium is about 4 gmole One reason for this is that while nitrogen is the most common constituent of the atmosphere only minute amounts of helium are found in the atmosphere Helium is found in natural gas deposits Why are only minute amounts of helium found in the atmosphere TB3 If the absolute temperature of a gas is doubled what is the change in the rms speed of its molecules TB3 At what temperature is the Fahrenheit temperature reading twice the Celsius temperature reading Page 23 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET Student 1 legible Name legible Section 01 or 02 1 A Fill in your student number last name and initials on the bubble sheet Do these clearly and carefully Errors will result in a rejected bubble sheet B Mark your exam version A or B C Hand write in your section number 001 or 002 in the section block on the bubble sheet D Fill in your name and section number on the exam booklet 2 While the exam is open book and open notes gno calculators or eletronic devices of any kind 1 you would be prudent to keep the use of these open book materials to a minimum These are concept questions that involve basic understanding and a few key equations There is essentially very little that you can look up from your book or notes There are essentially no quotequations to fmd quot You should have the basic concept equations in your head 3 It is recommended that you work in this booklet and wait until 10 20 minutes before the end of the period to mark your answer sheet Mark up the booklet any way you like It is recommended that you not waste time erasing This is a workbook 4 Make sure to use a soft 2 pencil to fill in the ovals on the bubble sheet Note that erasures 011 the bubble sheet can result in misreads and machine grading errors Please make sure of your answer before marking the bubble sheet 5 Ten minutes before the end of the period you will be reminded to begin to wrap things up and mark answers on your bubble sheet 6 Five minutes before the end of the period you will be reminded to wrap things up and turn in your booklet and answer sheet 7 The exam has 12 questions Each question is worth 9 points The maximum score is 108 It is the raw score that counts So you get a quotspotquot of 8 points A perfect score will net you 108 points toward the in term exam average You can miss 2 problems and still get an A miss 3 and still get B etc Addendum on academic integrity the academic integrity policy for this course is stated brie y in the syllabus and in detail in the separate document posted on RamCT Failure to abide by these rules will be considered academic dishonesty and will be dealt with according to university policy For exams exams are to be your own work and no consultation with other persons directly or indirectly is allowed You are not allowed to use any materials unless speci cally authorized to do by course policy or by the instructor It is never acceptable to copy work from another student Page 1 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET Possibly useful physics equations and connections Wherever needed take the gravitational acceleration parameter g as equal to 10 msz Derivative connections between 1D position xt velocity vxt and acceleration ax t d d axt Ema vx t Exa Use slopes 1nstead of der1vat1ves whenever poss1b1e Integral connections between 1D position xt velocity vxt and acceleration ax t a sz V m Avxt j axtdt Axt j moan ammo mea Use areas instead of integration whenever possible Centripetal acceleration ac and centripetal force F 5 both inward for a point mass m going mv2 2 around a circle ofradius R with a speed V a F0 R Newton s First Law An object in motion constant velocity tends to stay in motion same velocity dv d 2x Newton s Second Law quotF ma m Myquot Why 1s th1s equatlon 1n quotes 1 t Newton s Third Law For every force applied toin a system there is an equal and opposite force action reaction Hooke s law spring force law quotF kxquot Why is this equation in quotes nd e Xena Work force acting over a distance quotW I F d 7quot in 1D I dex Fmg gtlt distancequot start Xnm u 1 2 u Kmetlc energy K Emv Gravity work quotngv mghquot Spring work quotWsprmg kx2 quot end n 1 1 Work 7 k1net1c energy theorem work on a free mass quot I F d r quot mv nd mv m quot start 2 2 Maximum static friction force quot Stag2 ction uan quot stationary mass Kinetic friction force quotkae c motion uan quot moving mass dzx dv d mv d Momentum de ned from quotF maquot quotF m m p p mvquot d dt dt E d quotF maquot and actlonreact1on bas1s for momentum conservatlon 1 quotF d f dp Fd quot means that a force F1 acting over an incremental time dt on an object 1 causes a change in momentum dp for object 1 2 Action reaction says that the object 2 providing this force Page 2 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET suffers an equal and opposite force namely F 2 F1 and this force is applied for the same dt We have therefore dpz dp1 Elastic collisions momentum and kinetic energy are conserved in 1D the speed of approach for the oncoming masses in atwo mass collision equals the speed separation after the collision Inelastic collisions momentum is conserved but energy is not conserved Rotational dynamics based on TM and standard notation quotS Rt9quot quotdSdt v Rdt9dt Raquot dZSalt2 Ral219alt2 Rda2dt Raquot Torque for forces perpendicular to the lever arm pivot line etc quot r RF I aquot rotational analog to quotF maquot Moment of inertia Mass on the end ofa massless rod quot1 MR2 quot Rimmed wheel all mass uniformly distributed around circumference quotI MR 2 quot Rod of length L and mass M rotating about an axis at one end and perpendicular to the rod quot1 l3ML2 quot Uniform disk of radius R and mass M rotating about an axis through the center and perpendicular to the disk quotI l2MR 2 quot Torque and angular momentum vector connections quot 739 17 X R 107 61E dt Egtltj 1a3quot The vector cross product gtlt 6A3 direction of 21 x R by right hand rule Angular momentum conservation 3 0 3 L const since 3 51E dt General equilibrium condition quot2 F 0quot and quotZR 0quot Possibly useful math connections Sin 2 oppos1te 08 2 adjacent tan 2 oppos1te hypotenuse hypotenuse ad acent sin 30 1 2 cos 30 52 sin 30 cos 60 sin 60 cos 30 rule for complimentary angles sm45 J 21JE cos45 JE21JE tant9 sint9cost9 sin2t9cos2t9 l 2sint9cost9 sin 26 Derivative connection for xquot dixquot men 1 x Natural logarithm connection Idx x lnx Page 3 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET Disclaimer This Test Bank is provided with the sole aim of giving the student some advance idea of the kinds of questions that heshe will encounter on Exam 2 Some questions may also be taken from the previous Test Bank 1 for Exam 1 All of these questions are based on the TM Assignments in one form or another sometimes with modifications and sometimes with relayed questions and so on The student who has done the TM assignments and followed up with a review of the solution guides should be in a position to make effective use of this Test Bank to check their understanding as part of their nal review for the exam Students who have not done this may not fmd these Test Bank questions to be of much use The short time between now and the exam is insufficient to start from scratch and master all the concepts and applications embedded herein The questions given below do comprise the pool from which the exam questions were selected However the actual exam questions may differ to various degrees due to modi cations to ask somewhat different questions edits for clarity corrections of typos etc and so on The questions below have not been proofed in detail There may be typos and other issues Because the exam is based on these questions we will not be in a position to answer specific questions on any of them We would be happy to learn of any errors or typos Good luck on the exam on Thursday night lVIingzhong Wu and Carl Patton Page 4 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET John exerts a force Ofmagnitude F on the free end Ofthe rope Ifthe load moves up a distance 5 m how much work does John do on the rope Assume that the weight of the load is F g TBZ John exerts a force of magnitude F on the free end of the rope If the work done by John is 2F gh what distance does the load move up Note thath is the weight of the load TBZ You are in charge of installing a small foodservice elevator called a dumbwaiter in the food industry in a campus cafeteria The elevator is connectedby a pulley system to a motor as shown in the he motor raises and lowers the dumbwaiter The mass of the dumbwaiter is 100 kg In Operation it moves at a speed of 01 ms upward without accelerating If you purchase a motor with an ef ciency of 50 what minimum power rating should the motor have Assume that the pulleys are frictionless Where needed take the gravitational acceleration parameter g as equal to 10 msz Page 5 1 Mom mm m r PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBZ You are in charge Of installing a small foodservice elevator called a dumbwaiter in the food industry in a campus ca eteIia The elevator is connected by a pulley system to a motor as shown in the he motor raises and lowers the dumbwaiter The mass Of the dumbwaiter is 100 kg If you purchase a motor with a power rating Of 1 kW and an ef ciency Of80 what is the maximum speed at which the dumbwaiter can move upward without accelerating Assume that the pulleys are frictionless Where needed take the gravitational acceleration parameter g as equal to 10 msz TBZ You are in charge Of installing a small foodservice elevator called a dumbwaiter in the food industry in a campus cafe eria The elevator is connected by a pulley system to a motor as shown in the gure The motor raises and lowers the dumbwaiter The mass Of the dumbwaiter is 200 kg In operation it moves at a speed Of 05 ms upward without accelerating What is the power which the motor needs to provide Assume that the pulleys are frictionless Where needed take the gravitational acceleration parameter g as equal to 10 msz TBZ A block Of mass m on a horizontal frictionless tabletop is attached by a swivel to a spring that is attached to the ceiling as shown in the gure The vertical distance between the top Of the block and the ceiling is yo and the horizontal position is x When the block is at F0 the spring which has force constant k is completely unstressed What is the normal force appliedby the tabletop on the block as a function Ofx Page 6 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBZ A block of mass m on a horizontal frictionless tabletop is attached N r by a swivel to a spring that is attached to the ceiling as shown in t the gure The vertical distance between the top of the block and the ceiling is yo andthe horizontal position is x When the block is at F0 the spring is completely unstressed When the block is away from F0 the x component of the force on the block due to the spring is FX 78x3 If the block is released from rest at x xu where xu ltlt yu what is its speed when it reaches F0 Rig TBZ The gure shows the plot of a potentialenergy function Uversus x At which point does the force U associated with this function have the greatest magnitude TBZ The gure shows the plot of a potentialenergy function Uversus x Which point is a stable U equilibrium point Page 7 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBZ The gure shows the plot of a potentialenergy function Uversus x Which point is an unstable equilibrium point T A straight rod of negligible mass is mounted on a frictionless pivot as shown in the gure Blocks having masses m1 and m2 are attached to the rod at distances 1 and 2 The gravitational potential energy of the system changes with the angle Bmade by the rod andthe horizontal If mZ m13 and lZ 2l for what angle 8 is the potential energy a minimum TBZ A straight rod of negligible mass is mounted on a frictionless pivot as shown in the gure Blocks having masses m1 and m2 are attached to the rod at distances 1 and 2 The gravitational potential energy of the system changes with the angle Bmade by the rod andthe horizontal If mZ ml and lZ 211 for what angle 8 is the potential energy a maximum T A straight rod of negligible mass is mounted on a frictionless pivot as shown in the gure Blocks having masses m1 and m2 are attached to the rod at distances 1 and 2 The gravitational potential energy Uof the system changes with the angle Bmade by the rod andthe horizontal If mZ ml 2 kg and lZ 2l 05 m what is the potential energy ofthe system at an angle of 8 730 Choose U0 at Page 8 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBZ You have designed a novelty desk clock as shown in the gure You are worried that it is not ready for market because the clock itself might be in an unstable equilibrium vi con guration You decide to apply your knowledge of i potential energies and equilibrium conditions and anal z the situation The clock mass m is supported by two light cables running over the two frictionless pulleys of negligible diameter which are attached to counterweights that each has the same mass as the clock Find the value of y for which the potential energy of the system is a minimum TBZ A 8 kg block slides along a ictionless horizontal surface with a speed of 5 ms A er some distance it encounters a smooth frictionless inclined at 30 degrees to the horizontal What distance d up the ramp does the mass travel before momentarily coming to rest Where needed take the gravitational acceleration parameter g as equal to 10 msz TBZ A block of mass M slides along a frictionless horizontal surface with a speed v0 A er some distance it encounters an incline at 30 degrees to the horizontal with a rough surface and a coef cient of kinetic iction 16 l 3 Which expression below states correctly the conversion om kinetic energy for the mass at the bottom of the ramp and a combination of potential energy and friction work when it comes to rest a distance d up the ramp Hint What is the normal force when the mass is going up the ramp TBZ A block of mass M slides along a frictionless horizontal surface with aninitial speed v0 A er some distance it encounters a second horizontal section with a coef cient of kinetic friction bk 1 3 How much further call it a distance d does the mass slide before coming to rest Refer to the gure A 3 kg block is released from rest and slides down a frictionless ramp that starts 5 m above the horizontal It then slides 5 H m horizontally along a frictionless surface and encounters a spring with a spring constant of 400 Nm How much will the mass compress the spring distance x when it has come momentarily to rest wwNm Page 9 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIs EXAM BOOKLET WITH YOUR ANSWER SHEET TBZ Refer to the gure A 3 kg block is released from rest and slides down a frictionless rarnp that starts 5 m above the horizontal and continues along a frictionless horizontal surface What is the speed v Of the mass a er it reaches the horizontal surface Refer to the gure A 3 kg block is released from rest and slides down a frictionless rarnp that starts 5 In above the horizontal and continues along a rough horizontal surface With a coef cient Of kinetic friction k of 12 What is kinetic energy K Ofthe mass a er it has traveled a distance Of 103 m along the horizontal surface Refer to the gure A mass is released from the top Of a ramp that is a distance H above ground level Assume that this height is adequate for the mass to make it around the vertical loop Ofradius R not labeledin the gure The entire rail track is frictionless What is the normal force Fn Of the rail on the mass When the mass is at the very top Ofthe loop Refer to the gure A mass is released from the top Of a ramp that is a distance H above ground level Assume that this height is adequate for the mass to make it around the vertical loop Of radius R not labeledin the gure The entire rail track is frictionless What is the normal force Fn Of the rail on the mass When the mass is at the very bottom Of the loop Page 10 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET Refer to the gure A mass is released from the top Of an entrance ramp that is a distance H above ground level Assume that this height is adequate for the mass to make it around the vertical loop Of radius R not labeled in the gure There is also an exit ramp a height R above the bottom level Of the ramploop structure not labeled in the gure The entire rail track is frictionless What is the exit speed 11 Of the mass at the end Of the exit ramp TBZ Refer to the gure A 2 kg block is released from rest and slides down a frictionless ramp that starts 3 m above the horizontal and then continues along a rough horizontal surface With a coef cient Of kinetic friction yk until it comes to rest 9 m away from the end Of m 20 kg g u u m the ramp Where needed take the gravitational acceleration parameter g as equal to 10 msz What is kinetic energy K3 Ofthe mass after it has traveled a distance Of 3 m along the horizontal surface TBZ Refer to the gure A 2 kg block is released from rest and slides down a frictionless ramp that starts 3 m above the horizontal and then continues along a rough horizontal surface With a coef cient Ofkinetic ictionyk until it comes to rest 9 m away from the end Of m 20 kg the ramp Where needed take the gravitational acceleration parameter g as equal to Page 11 10 msz What is yk PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBZ Refer to the gure A 2 kg block is released from rest and slides down a frictionless ramp that starts 3 m above the horizontal and then continues along a rough horizontal surface with a coef cient ofkinetic frictionyk until it comes to rest 9 m away from the end of e ramp Where needed take the gravitational acceleration parameter g as equal to 10 msZ If the initial angle of the ramp at the start ofthe fall is 30 degrees from the vertical what is the initial acceleration no down the ramp TBZ Refer to the gure A block ofmass m is connected to the left end of spring of force Release Posmon constant k The right end of the spring is connected to a rigid wall The coef cients of static and kinetic friction of the horizontal surface on which the mass rests are 5 and yk respectively The spring is initially unstretched The mass is then pulled away from the wall a distance do such that if released the return spring force will just barely overcome the static friction force holding the mass back that is do is equal to ySmgk plus a little bi as discussed inlecture What is the initial acceleration no at release Hint What is the friction force backward when the mass is moving TBZ Refer to the gure A block ofmass m is connected to the left end of spring of force Release Posmon constant k The right end of the spring is connected to a rigid wall The coef cients of static and kinetic friction of the horizontal surface onwhich the mass rests are 5 and yk respectively The spring is initially unstretched The mass is then quotT ma pulled away from the wall a suf cient distance do such that when released the mass is pulled back toward the wall and comes to rest back at the original position of zero stretch What is do Page 12 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THrs EXAM BOOKLET WITH YOUR ANSWER SHEET TBZ Refer to the gure A block Ofmass m is connected to the left end Of spring Of force constant k The right end Of the spring is Release position connected to a rigid wall The coef cients 7 gt It W V K H N i Ofstatic and kinetic friction Ofthe quotL H L5 3quot if My v r i horizontal surface on which the mass rests i R1 are 5 and k respectively The spring is initially unstretched The mass is then I x pulled away from the wall a suf cient distance do which is suf cient that when released the mass is pulled back toward the wall and actually passes the initial unstretched position while still moving What is the kinetic energy K 0 Of the mass as it passes the initial unstretched position TBZ Refer to the gure A car with a total mass B m 1000 kg car plus c passengers travels along I D F the roller coaster structure G g 30 3 indicated The starting T T T platform at A and straight at sections at E and G are 10 m above the ground The launch velocity v is 12 ms as indicated Point D is at ground level The radius Ofcurvature for the dip at D and the curve at F is the same R 25 m What is the height at Point B relative to the ground for the car to barely make it over the top TBZ Refer to the gure A car with a total mass m 1000 kg car plus passengers travels along the roller coaster structure 0 r 3039 indicated The starting 3 platform at A and straight at sections at E and G are 10 m above the ground The launch velocity v is 12 ms as indicated Point B is just high enough to let the car barely make it over the top Point D is at ground level The radius Of curvature for the dip at D and the curve at F is the same R 25 m For which curve Points B D or F is the net centripetal force On the car the greatest Page 13 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET Refer to the gure A car With atotal mass 12 5 B m 1000 kg car plus A passengers travels along the roller coaster structure G g 30 B indicated The starting T T T platform at A and straight at sections at E and G are 10 m above the ground The launch velocity v is 12 ms as indicated Point B is just high enough to let the car barely make it over the top Point D is at ground level The radius Of curvature for the dip at D and the curve at F is the same R 25 In What is the accelerationag on the downward sloping run along C TBZ Refer to the gure A stunt person whom we will call the slider slides down a frictionless hemispherical surface with a radius H Ignore the bungee cord component Of the TM problem and just consider the person as a sliding mass going down the curved surface Of radius H Heshe has a mass m and starts at rest plus a little nudge from the top 8 0 in the gure What is the speed function for the slider denoted as v8 as heshe moves down the curved surface Hint Use energy conservation Page 14 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THrs EXAM BOOKLET WITH YOUR ANSWER SHEET TBZ Refer to the gure A stunt person whom we will call the slider slides down a frictionless hemispherical surface with a radius H Ignore the bungee cord component Of the TM problem and just consider the person as a sliding mass going down the curved surface Of radius H Heshe has amass m and starts at rest plus a little nudge from the I top 8 0 inthe gure What is the normal force 39 H on the slider from the curved surface denoted as I F n 8 as heshe moves down the curved surface Hint to get started How can you convert a kinetic 9 energy Emv2 for an Object traveling around a circle Of radius R into a centripetal force Where does this force come from for the geometry Of this problem TBZ Refer to the gure A stunt person whom we will call the slider slides down a frictionless hemispherical surface with a radius H Ignore the bungee cord component Of the TM problem and just consider the person as a sliding mass going down the curved surface Of radius H Heshe has amass m and starts at rest plus a little nudge from the top 8 0 in the gure What is the tangential acceleration response call it L1th 8 Of the slider down and parallel to the curved surface as heshe moves down the curved surface Hint Look at functional dependences in known limits TBZ The gure shows the behavior Of a projectile just a er it has broken l up into three pieces If the projectile travels to the right with a speed Of 25 ms before it broke up what is the magnitude Of V3 Page 15 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THrs EXAM BOOKLET WITH YOUR ANSWER SHEET up into three pieces What was the magnitude Of the momentum Of TBZ The gure shows the behavior Of a projectile just a er it has broken the projectile the instant before it broke up I 3 TBZ A wedge Of mass M is placed On a frictionless horizontal surface and a block Ofmass m is placed on the wedge which also has a frictionless surface The blocks center Of mass moves downward a distance 11 as the block slides from its initial position to the horizontal oor As the block and the wedge separate from each other and go their own ways what is the kinetic energy Of the block 1mm TBZ A wedge Of mass M is placed on a frictionless horizontal mum surface and a block Ofmass m is placed on the wed e which also has a frictionless surface The blocks center Of mass moves downward a distance 11 as the block slides from its initial position to the horizontal oor As the block and the wedge separate from each other and go their Final own ways what is the kinetic energy Ofthe wedge Page 16 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBZ A wedge Of mass M is placed on a frictionless horizontal hum surface and a block Ofmass m is placed on the wed e which also has a frictionless surface The blocks center Of mass moves downward a distance 11 as the block slides from its initial position to the horizontal oor As the block and the wedge separate from each other and go their own ways what is the speed Of separation Assume 8m TBZ Ablock Ofmass m1 20 kg slides along a frictionless table with a speed 10 ms Ly k ltz 10 ms Of50 ms Directlyinfront Ofit and U H quotAquot 1 quot moving in the same direction with a speed Of20 ms is a block Ofmass m2 40 kg A massless spring that has a force constant F1120 Nm is attached to the second block as in the gure During the collision the spring is compressed A er the collision the two blocks separate again What is the speed Of separation a er the collision TBZ Ablock Ofmass ml 10 kg slides along a frictionless table with a speed J0 ms k in N N A 30 ms Of40 ms Directly in front Ofit and Lquot J39L DL Litth moving in the same direction with a speed Of10 ms is a block Ofmass m2 20 kg A massless spring that has a force constantFIOOO Nm is attached to the second block as in the gure During the collision the spring is compressed by a maximum amount Of Ax and the two blocks move in the same velocity After the collision the blocks separate again What is the speed Of the blocks during the collision Page 17 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THrs EXAM BOOKLET WITH YOUR ANSWER SHEET TBZ A block ofmass m1 l 0 kg slides 7c along a ictionless table with a speed W m P 1 1 1a N mins of40 ms Directly in front ofit and u 39 L quot quot moving in the same direction with a speed of l 0 ms is a block ofmass m2 20 kg A massless spring that has a force constant F1000 Nm is attached to the second block as inthe gure During the collision the spring is compressed by a maximum amount of Ax and the two blocks move inthe same velocity After the collision the blocks separate again What is the elastic potential energy stored in the spring during the collision TBZ A bullet of mass m is red vertically from Pa m Pl 39wnod below into a thin horizontal sheet of plywood I V of mass M that is initially at rest supported M r by a thin sheet of paper as shown in the Hle gure The bullet punches through the plywood which rises to a height H above the I paper before falling back down What is the magnitude of the momentum of the bullet right before it hits the plywood TBZ A bullet of mass m is red vertically from below into a thin horizontal sheet of k plywood ofmass Mthat is initially at rest i i M i J supported by a thin sheet of paper as shown mu in the gure The bullet punches through the plywood which rises to a height H above the paper before falling back down The bullet continues rising to a height 11 above the paper What is the total kinetic energy of the bullet and the plywood right a er the bullet punches through the plywood I39Jper I lywnud Page 18 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBZ In a Onedimensional elastic collision if the mass and velocity Of Object 1 are m m0 and VII 2v0 and the mass and velocity Of Object2 are m2 2m and vzl v0 thenthe nal velocity Of object 1 is TBZ In a Onedimensional elastic collision ifthe mass and velocity Of object 1 are m 2m and vll 2 and the mass and velocity Of Object 2 are m2 3mg and vz v0 then the nal velocity Of Object 1 is Refer to the gure A 2 kg mass is overtaking a 3 kg mass with velocities as shown What is the center Of mass velocity vcm for this system TBZ Refer to the gure A 2 kg mass is overtaking a 3 kg mass with velocities as shown A er the collision the 3 kg mass is moving to the right at 42 ms 215 ms What is the impulse 13 Ap3 change in momentum delivered to the 3 kg mass by the 2 kg mass TBZ Refer to the gure A 2 kg mass IS overtaking a 3 kg mass with velocities as shown A er the collision the 3 kg mass is moving to the right at 42 ms 215 ms What is the velocity V2 Of the 2 kg mass alter the collision Page 19 El 50 mS PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBZ Refer to the gure A 5 kg mass at a speed of 2 ms travels horizontally and approaches another 5 kg mass a little off center as shown The initial mass glances off at a de ection angle of 30 toward the vertical up direction and the other mass is de ected down by 60 as shown Which of the following is true TBZ Refer to the gure A 5 kg mass at a Speed of 2 ms travels horizontally and approaches another 5 kg mass a little off center as shown The initial mass glances off at a de ection angle of 30 toward the vertical up direction and the other mass is de ected down by 60 as shown Which of the following is true TBZ Refer to the gure A 5 kg mass at a speed of 2 ms travels horizontally and approaches another 5 kg mass a little off center as shown The initial mass glances off at a de ection angle of 30 toward the vertical up direction and the other mass is de ected down by 60 as shown What is the center mo mass velocity Um of the system Page 20 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBZ A rocket has a dry fuel free mass M 0 and an initial fuel load of mass M F The rocket engine has a fuel burn rate of R0 kgs The exhaust gases leave the rocket nozzle at a speed uo The rocket is launched vertically y direction and stays close enough to the earth that the usual gravitational acceleration constant g remains valid Which of the equations below is a valid equation for the mass of the rocket M t as a function of time t TBZ A rocket has a dry fuel free mass M 0 and an initial fuel load of mass M F The rocket engine has a fuel burn rate of R0 kgs The exhaust gases leave the rocket nozzle at a speed uo The rocket is launched vertically y direction and stays close enough to the earth that the usual gravitational acceleration constant g remains valid The quotF Ma equation for the rocket motion is given by 7M0 MF 7R0 gR0u0 M0 MF 7R0 dvy dt Which term or terms On the le side of this equation represents the thrust Fthmm of the rocket TBZ A rocket has a dry fuel free mass M 0 and an initial fuel load of mass M F The rocket engine has a fuel burn rate of R0 kgs The exhaust gases leave the rocket nozzle at a speed uo The rocket is launched vertically y direction and stays close enough to the earth that the usual gravitational acceleration constant g remains valid The quotF Ma equation for the rocket motion is given by 7M0 MF 7R01gR0u0 M0 MF 7R01dvy dt In this equation the Rouo term on the le represents the thrust term that is the upward force On the rocket due to the expelled fuel What is the physical basis of this term TBZ Refer to the gure A 1 kg steel ball mass 1 On a 2 m long massless rod with a frictionless pivot swings down as indicated and suffers an elastic collision with the 1 kg block that sits on a friction surface mass 2 Take the x 7 directed velocity of the ball just as it approaches the block at the end of the swing down as v11 Take the velocities of the ball and the block just a er the elastic collision as v1 f and v f respectively The friction surface has a coef cient of kinetic friction yk 02 Where needed take the gravitational acceleration parameter g as equal to 10 msz What is v11 Page 21 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WI TBZ Refer to the gure A 1 kg steel ball mass 1 on a 2 m long massless rod with a frictionless pivot swings down as indicated and suffers an elastic collision with the 1 kg block that sits on a friction surface mass 2 Take the x 7 directed velocity of the ball just as it approaches the block at the end of the swing down as v11 Take the velocities of the ball and the block just a er the elastic collision as v1 f and v f respectively The friction surface has a coef cient ofkinetic friction yk 02 W39her acceleration parameter g as equal to 10 msz What is v 2f TH YOUR ANSWER SHEET e needed take the gravitational Refer to the gure A 1 kg steel ball mass 1 on a 2 m long massless rod with a frictionless pivot swings down as indicated and suffers an elastic collision with the 1 kg block that sits on a friction surface mass 2 Take the x7 directed velocity of the ball just as it approaches the block at the end of the swing down as v11 Take the mm velocities of the ball and the block just a er the elastic collision as v1 f and v f respectively The friction surface has a coef cient ofkinetic friction yk 02 W39her e needed take the gravitational acceleration parameter g as equal to 10 msz How far a distance d does the block slide a er the collision TBZ Refer to the gure In the slingshot effect a rocket of some mass m passes close to and behind a very massive object such as saturn ofmass M with M gtgtm such that it is de ected roughly back in the opposite 39 ection from its approach This elastic collision gives a kick to the speed of the rocket Viewed as a 1D problem with positive x to the W mmt Hum5 le the direction of the planet s motion what is the approximate center of mass velocity vkm Page 22 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBZ Refer to the gure In the slingshot effect a rocket Of some mass m passes close to an a r behind a very massive Object such as saturn L Ofmass M with M gtgtm such that it is quot de ected roughly back in the Opposite direction from its approach This elastic collision gives a kick to the speed Of the rocket Viewed as a 1D problem with positive x to the le the direction Of the planet s motion what is the velocity Of separation 11W for the two Objects a er the collision Hint Remember that for 1D two mass elastic collisions the separation speed equals the closing speed TBZ Refer to the gure In the slingshot effect a rocket Of some mass m passes close to and i r behind a very massive Object such as saturn w mm D 0 mass W1 gtgt m such that it is de ected roughly back in the Opposite direction from its approach This elastic collision gives a kick to the speed Of the rocket Viewed as a 1D problem with positive x to the le the direction Of the planet s motion what is the new velocity Of the rocket vkmk or v in the gure a er the interaction Hint Remember that for 1D two mass elastic collisions the separation speed equals the closing speed TBZ Staning from rest and rotating at constant angular acceleration a disk takes 10 revolutions to reach an angular speed a How many additional revolutions at the same angular acceleration are required for it to reach an angular speed Of 3a TBZ Starting from rest and rotating at constant angular acceleration a disk takes 10 revolutions to reach an angular speed a How many revolutions at the same angular acceleration are required for the dist to start from rest and reach an angular speed Of 3a TBZ Staning from rest and rotating at constant angular acceleration a disk takes 10 revolutions to reach an angular speed a 207 rads What is the angular acceleration Page 23 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBZ Consider a disk Of mass M and radius R that is rolling without slipping What is the ratio Of the translational kinetic energy Of the disk to its rotational kinetic energy TBZ Consider a disk Of mass M and radius that is rolling at a constant angular speed Of a without slipping What is the difference betvveenthe translational kinetic energy and rotational kinetic energy Of the disk TBZ Refer to the gure a shows a spool is free to rotate about a xed axis In this case pulling on the string wrapped aroundthe axle Of the spool causes the spool to rotate in a counterclockwise direction as shown However if the spool is set On a horizontal tabletop as shown in b with suf cient friction to avoid slipping pulling On the string causes the spool to rotates in a clockwise direction and roll to the right In the b diagram assume that the string is pulled horizontally NOT at an angle as shown by a force F In this case what is the angular acceleration Of the spool UseM as the mass Of the spool R as the radius Of the spool and r as the radius Of the axle Assume the spool consists Of a uniform disk and amassless axle attached to its center Hint Work with a pivot axis for the circular acceleration a at the point Of contact between the wheel and the surface and use the parallel axis theorem to Obtain the moment Of inertia Of the spool for this axis TBZ Refer to the gure a shows a spool is free to rotate about a xed axis In this case pulling on the string wrapped aroundthe axle Of the spool causes the spool to rotate in a counterclockwise direction as shown However if the spool is set On a horizontal tabletop as shown in b with suf cient friction to avoid slipping pulling On the string causes the spool to rotates in a clockwise direction and roll to the right In the b diagram assume that the string is pulled horizontally NOT at an angle as shown by a force F In this case what is the linear acceleration a Of the spool to the right Use M as the mass Of the spool R as the radius Of the spool and r as the radius Of the axle Assume the spool consists Of a uniform disk and m a massless axle attached to its center Hint Work with a pivot axis for the circular acceleration a at the point Of contact between the wheel and the surface and use the parallel axis theorem to Obtain the moment Of inertia Of the spool for this axis Solve for a and then a Page 24 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET A Wheel released from rest is rotating with constant angular acceleration of 41 radSZ At 40 s a er the release how many revolutions has it completed TBZ A Wheel released from rest is rotating With constant angular acceleration of 4 radSZ At 50 s a er the release What is the linear speed of a point 010 m from the axis ofrotation TBZ Star A orbits the earth With an orbital period of 16 hours Star E orbits the earth With an orbital period of 20 hours When Start A makes 5 revolutions how many revolutions does Start B make a 2 reV c 5 rev b 4 rev d 8 rev TBZ Refer to the gure We have four particles With point masses m1 m2 m3 m4 1 kg connected With rigid massless rods in the shape of a square With side lengths of 2 m mass centertocenter The masses in the gure are shown as balls for illustration purposes only for this problem consider them as point masses What is the moment of inertia 1 for rotations about the y 7 axis TBZ Refer to the gure We have four particles With point masses m1 m2 m3 m4 1 kg connected With rigid massless rods in the shape of a square With side lengths of 2 m mass centertocenter The masses in the gure are shown as balls for illustration purposes only for this problem consider them as point masses What is the moment of inertia IZ for rotations about the 27 axis Page 25 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBZ Refer to the gure We have four particles with point masses m1 m2 m3 m4 1 kg connected with rigid massless rods in the shape Of a square with side lengths Of 2 m mass centertOcenter The masses in the gure are shown as balls for illustration purposes only for this problem consider them as point masses What is the moment Of inertia If for rotations about an axis through the center and parallel to the z xis Consider a right circular cone which is solid and has a total mass density per unit volume p kgm3 a height H and a top radius R Let the cone axis be along the y7 axis with the tip at y 0 and the circular end at y H Keep in mind that the moment Ofinertia Of athin disk for rotations about an axis through its center and perpendicular to the disk is given by I 011 g 1 2MmskR lSk Which integral equation below will give the moment Of inertia Of the cone 15012 for rotations about the y7 axis The quotxquot in all Of these expressions corresponds to the radii Of the incremental disks located at some position y Of thickness dy and a radius x de ned by xy RyH Consider two right circular cones cone A which is solid and cone B which is hollow and has mass only around the shell Of the cone Both cones have the same mass M the same height H and the same top radius R Let the cone axes be along the y7 axis with the tip at y 0 and the circular end at y H Which cone will have the largest moment Of inertia TBZ Consider a right circular cone which is solid and has a total mass density per unit volume p kgm3 a height H and a top radius R Let the cone axis be along the y7 axis with the tip at y 0 and the circular face end at y H You intend to calculate the moment Of inertia Of the cone 15012 for rotations about y faxis by setting up an integral along y from y 0 the tip to y y H the face Ofthe form 150 I rzdm where r corresponds to the radius Ofa y differential disk located at some position y Of thickness dy and with a radius r de nedby ry Ry H Which Of the expressions below for the mass dm Ofthese differential disks is correct Page 26 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET Refer to the gure A uniform rod oflength L and mass M is pivoted at one end and suspended so that it is free to rotate as indicate A student strikes the rod with a sharp horizontally directed blow with a force F0 applied at position x for a very short time At Short means that the rod has not rotated by any appreciable angle during the strike From the rotational 4 I at equation for s stem durin the time the force is applied one can get the horizontal acceleration of the centerof mass point on the rod at xm L2 taken as am in terms of F0 Which relation below expresses this connection TBZ Refer to the gure A uniform rod oflength L and mass M is pivoted at one end and suspended so that it is free to rotate as indicated A student strikes the rod with a sharp horizontally directed blow with a force F0 applied at position x for a very short time At Short means that the rod has not rotated by any appreciable angle during the strike During the action of F0 there is an additional horizontal force on the rod at the pivot not shown in the diagram that we will denote as F p What is the appropriate horizontal quotF ma equation for the acceleration am of the centerofmass position xm L 2 during the action of F0 Take F0 and FF as the magnitudes ofthese forces TBZ Refer to the gure A uniform rod oflength L and mass M is pivoted at one end and suspended so that it is free to rotate as indicated A student strikes the rod with a sharp horizontally directed blow with a force F0 applied at position x for a very short time At Short means that the rod has not rotated by any appreciable angle during the strike From the rotational 4 I at equation for system during the time the force is applied one can get the angular acceleration do of the rod about the pivot What is do Page 27 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBZ Refer to the gure The wheel structure has to separate wheels that rigidly attached to each other and rotate in common Take the tensions in the ropes connecting m1 and m 2 to the wheel structure as T1 and T 2 respectively The gravity quotmgquot forces not shown are down Of course For visualization purposes assume mass m1 is suf ciently large to cause any rotation Of the wheel structure to go counter clockwise What is the magnitude Of the net torque on the wheel structure TBZ Refer to the gure The wheel structure has to separate wheels that rigidly attached to each other and rotate in common For visualization purposes assume mass m1 is suf ciently large to cause any rotation Of the wheel structure to go counter clockwise If the counter clockwise rotational acceleration Of wheel structure is aw what are e inear accelerations Of the two masses a1 down for m1 and a up for m 2 TBZ Refer to the gure The wheel structure has to separate wheels that rigidly attached to each other and rotate in common For visualization purposes assume mass m1 is suf ciently large to cause any rotation Of the wheel structure to go counter clockwise Take the mass Of the wheel as M W and the moment Of inertia for rotations about the axle as W Take the tensions in the ropes connecting m1 and m 2 to the wheel structure as T1 and T 2 respectively Take the angular acceleration Ofthe wheel as aw What is the rotational quotF ma equation eg the quotr Ia equation for the wheel structure Page 28 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBZ Refer to the gure A uniform cylinder Ofmass m1 and radius R rotates in a frictionless pocket as shown A string wrapped around the cylinder is tied to mass m 2 that rests on a frictionless incline at an angle 8 to the horizontal The system is released from rest when the right most edge Of the mass is a height h as shown If the potential energy U Of m 2 is taken to be equal to ngh relative to U 0 when the right edge Of the mass is at the bottom Of the incline which Of the following equations express energy conservation from the start Of the motion to the end point with the mass at the bottom with a speed vzf and the cylinder at the top with a corresponding angular velocity TBZ Refer to the gure A uniform cylinder Ofmass m1 and radius R rotates in a frictionless pocket as shown A string wrapped around the cylinder is tied to mass m that rests on a frictionless incline at an angle 8 to the horizontal The system is released from rest when 1 the right most edge Of the mass is a height h as shown IL During the motion take the tension in the rope as T 0 and the acceleration of m down the incline as no Which Ofthe proposed quot4 Int equations below a er cancellation Of common terms is correct TBZ Refer to the gure A uniform cylinder Of mass m1 m and radius R rotates in a frictionless pocket as shown A string wrapped around the cylinder is tied to mass m 2 that rests on a frictionless incline at an angle 8 to the horizontal The system is released from rest when I the right most edge Of the mass is a height h as shown 9 During the motion take the tension in the rope as T 0 and the acceleration of m down the incline as no Which Ofthe proposed quotF ma equations below is correct Page 29 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBZ Refer to the gure A uniform cylinder Ofmass m1 and radius R rotates in a frictionless pocket as shown A string wrapped around the cylinder is tied to mass m 2 that rests on a frictionless incline at an angle 8 to the horizontal The system is released from rest when the right most edge Of the mass is a height h as shown During the motion take the tension in the rope as T 0 and the acceleration of m down the incline as no Which Of the proposed quotF ma equations applies to the total system TBZ The spin angular momentum vector for a spinning wheel is parallel with its axle and is pointed west TO cause this vector to rotate toward the south in which direction must a force be exerted on the west end Ofthe axle TBZ The spin angular momentum vector for a spinning wheel is parallel with its axle and is pointed east Toward which direction will this vector rotate if a force pointing down is exerted on the east end Of the axle TBZ The spin angular momentum vector for a spinning wheel is parallel with its axle and is pointed north Toward which direction will this vector rotate if a force pointing up is exerted on the north end Ofthe axle TBZ The angular momentum Of the propeller Of a small singleengine airplane points forward The propeller rotates clockwise if viewed from behind If the plane is ying horizontally and suddenly turns to the left to which side does the nose Of the plane tend to veer TBZ The angular momentum Of the propeller Of a small singleengine airplane points forward The propeller rotates clockwise if viewed from behind If the plane is ying horizontally and the nose Of the plane suddenly turns downward to which side does the nose Of the plane tend to veer Page 30 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBZ John is sitting on a spinning piano stool with his arms extended When he has his arms folded what happens to his kinetic energy TBZ John is sitting on a spinning piano stool with his arms extended When he has his arms folded which of the following decreases TBZ John is sitting on a spinning piano stool with his arms folded When he extends his arms out to his sides which of the following remains the same TBZ IfZlf7k and 2j397kwhatis 21x3 TBZ lflzlj39ilg and Iwhatisthelengthofthevector AXE TBZ If A2fjgtk and kwhatis Ax Refer to the gure A block of mass m sliding on a frictionless table is attached to a string that passes through a hole through the center of the table The block is sliding around in a circle at a speed v0 in a circle of radius r0 if 7 gure shows simply r replace with re Two vector i J centripetal force for the circular motion and a downward forces are shown the rope tension i that provides the m J T Li 4 4 J J L force 1 on the rope under the table provided by an invisible student What is the angular momentum L 0 of the rotational motion in rads Page 31 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBZ Refer to the gure A block Ofmass m sliding on a m frictionless table is attached to a string that passes through a hole through the center Of the table The block is sliding around in a circle at a speed v0 ina circle Of radius r0 7 gure shows simply r replace with r0 Two vector forces l are shown the rope tension f that provides the centripetal i F force for the circular motion and a downward force 1 on T T the rope under the table providedby an invisible student Which way does the angular momentum for the system point TBZ Refer to the gure A block Ofmass m sliding on a frictionless table is attached to a string that passes through a R hole through the center Of the table The block is sliding 7 T 39 around in a circle at a speed v0 in a circle Of radius r0 quot gure shows simply r replace with r0 Two vector t 1 7i w 1 forces are shown the rope tension T that provides the l I centripetal force for the circular motion and a downward 7 ce 17 on the rope under the table provided by an invisible student If the student pulls quasistatically on the rope with avariable force as needed and pulls the mass in to a circle Ofa radius Of Onethird Ofthe initial radius eg r1 r0 3 what is the new speed VI of rotation TBZ Refer to the gure A block Ofmass m sliding on a frictionless table is attached to a string that passes through a 5 hole through the center Of the table The block is sliding quot V T around in a circle at a speed v0 ina circle Of radius r0 39 7 gure shows simply r replace with r0 Two vector i J i forces are shown the rope tension T that provides the I F I centripetal force for the circular motion and a downward force I7 on the rope under the table provided by an invisible student If the student pulls quasistatically on the rope with avariable force as needed and pulls the mass in to a circle with a smaller radius r as heshe pulls how does the force change as the radius Of rotation gets smaller Page 32 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU lVl39UST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TB2 Refer to the gure A uniform solid wheel of mass M and radius R is set spinning at angular frequency an L for angular momentum and placed with the left end of the axle set on a pivot as shown When the wheel is released point A at the right end of the axle will initially move in which of the four directions indicated Hint Use an appropriate form of the right hand rule to get the direction of the angular momentum vector E Then use the vector cross product for the appropriate moment arm vector and the cm located on the wheel axis and a little to the left of the wheel proper Mg force vector to obtain the direction of the torque quot 739 F X quot Then use 3 di 11 to determine how the E changes with time Hint TB2 Refer to the gure A uniform solid wheel of mass M and radius R is set spinning at angular frequency an L for angular momentum and placed with the left end of the axle set on a pivot as shown What is the direction of the torque on the gyroscope when the system is released Hint Use the vector cross product for the appropriate moment arm vector from the pivot to the center of mass of the gyroscope located on the wheel axis just at the middle of the wheel proper and the Mg force vector applied at the center of mass to obtain the direction of the torque quotf F X 15quot TB2 Refer to the gure A uniform solid wheel of mass M and radius R0 is set spinning at angular frequency an L for angular momentum and placed with the left end of the axle set on a pivot as shown What is the magnitude of the angular momentum L of the spinning wheel TB2 Refer to the figure A box with a mass M a length L and a L height H rests on a horizontal slab that is accelerating to the right with some value aY The boxslab contact surfaces M have friction that is sufficient to keep the box from sliding What is the maximum value of the acceleration akmax F f no loquot that can occur before the box tips Hint Instead of using an Slab accelerating to the right at a acceleration aY to the right this problem may be easier to gt a visualize in terms of an effective gravity force on the box pulling to the left of MaY Page 33 PH141 Fall 2011 Test Bank 2 Test version X mark this version on your answer sheet YOU MUST RETURN THIS EXAM BOOKLET WITH YOUR ANSWER SHEET TBZ A large truck has its front and back axles separated by a distance D and 13 of the weight is supported on the front axle Where is the centerofmass of the truck located TBZ Refer to the gure The gravity board to the right provides a simple way to determine the center of mass of a person The board itself is centered on the two supports that are separated by a distance of 2 m The right fulcrum has a scale underneath The person is known to have a mass of 100 kg When the person is positioned on the board with his head lined up with the le fulcrum the weight measured on the right fulcrumscale advances by 375 N from its reading for the board alone Where is the center 2w ofmass location of the person relative to the le fulcrum the one with no scale Wherever needed take the gravitational acceleration parameter g as equal to 10 msz Hint Use rotational equilibrium no torque and a pivot at the le fulcrum Page 34

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