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# University Physics I PHYS 1321

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This 128 page Class Notes was uploaded by Kayley Corwin on Saturday September 19, 2015. The Class Notes belongs to PHYS 1321 at University of Houston taught by Staff in Fall. Since its upload, it has received 7 views. For similar materials see /class/208346/phys-1321-university-of-houston in Physics 2 at University of Houston.

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Date Created: 09/19/15

University Physics 132 YoungFreedman Chapter 3 Motion in Two or Three Dimensions 31 Conceptual Questions 1 Shown below are the velocity and acceleration vectors for a person in several different types of motion In which case is the person slowing down and turning to his right if 1 13 B if li C T i7 D 2139 E V 4 p 3 Answer B 2 While an object is in projectile motion with upward being positive with no air resistance A the horizontal component of its velocity remains constant and the horizontal component of its acceleration is equal to g B the horizontal component of its velocity remains constant and the vertical component of its acceleration is equal to g C the horizontal component of its velocity remains constant and the vertical component of its acceleration is equal to zero D the vertical component of both its velocity and its acceleration remain constant E the vertical component of its velocity remains constant and the vertical component of its acceleration is equal to g Answer B Var l 3 For general projectile motion when the projectile is at the highest point of its trajectory A its acceleration is zero B its velocity is perpendicular to the acceleration C its velocity and acceleration are both zero D the horizontal component of its velocity is zero E the horizontal and vertical components of its velocity are zero Answer B Var l 4 Alice and Tom dive from an overhang into the lake below Tom simply drops straight down from the edge but Alice takes a running start and jumps with an initial horizontal velocity of 25 ms Neither person experiences any signi cant air resistance Just as they reach the lake below A the speed of Alice is larger than that of Tom B the splashdown speed of Alice is larger than that of Tom C they will both have the same speed D the speed of Tom will always be 98 ms larger than that of Alice E the speed of Alice will always be 25 ms larger than that of Tom Answer A Var l 5 Alice and Tom dive from an overhang into the lake below Tom simply drops straight down from the edge but Alice takes a running start and jumps with an initial horizontal velocity of 25 ms Neither person experiences any signi cant air resistance Compare the time it takes each of them to reach the lake below A Alice reaches the surface of the lake rst B Tom reaches the surface of the lake rst C Alice and Tom will reach the surface of the lake at the same time Answer C Var l 6 Jan and Len throw identical rocks off a tall building at the same time The ground near the building is at Jan throws her rock straight downward Len throws his rock downward and outward such that the angle between the initial velocity of the rock and the horizon is 30 Len throws the rock with a speed twice that of Jan s rock Ifair resistance is negligible which rock hits the ground rst A They hit at the same time B J an s rock hits rst C Len39s rock hits rst D It is impossible to know from the information given Answer A Var l 7 A monkey is sitting at the top of a tree 20 m above ground level A person standing on the ground wants to feed the monkey He uses a bow and arrow to launch the food to the monkey If the person knows that the monkey is going to drop from the tree at the same instant that the person launches the food how should the person aim the arrow containing the food Air resistance is small enough to be ignored A He should aim it at the monkey B He should aim it below the monkey C He should aim it above the monkey Answer A Var l 8 A pilot drops a package from a plane ying horizontally at a constant speed Neglecting air resistance when the package hits the ground the horizontal location of the plane will A be behind the package B be over the package C be in front of the package D depend of the speed of the plane when the package was released Answer B Var l 9 For an object in uniform circular motion its velocity and acceleration vectors are always perpendicular to each other at every point in the path A True B False Answer A Var l 10 If an object travels at a constant speed in a circular path the acceleration of the object is A larger in magnitude the smaller the radius of the circle B in the same direction as the velocity of the object C smaller in magnitude the smaller the radius of the circle D in the opposite direction of the velocity of the object E zero Answer A Var l 11 Point P in the gure indicates the position of an object traveling at constant speed clockwise around the circle Which arrow best represents the direction of the acceleration of the object at point P A Answer D Var l 12 If you set the cruise control of your car to a certain speed and take a turn the speed of the car will remain the same Is the car accelerating 3 2 Problems 1 Object A has a position as a function of time given by rAt 300 msti 100 ms2t2j Object B has a position as a function oftime given by 30 400 msti 100 ms2t2j All quantities are SI units What is the distance between object A and object B at time t 300 s A 346 m B 150 m C 183 m D 346 m E 298 m Answer C Var 5 2 An object has a position given by i 20 m 500 msti 30 m 200 ms2t2i where quantities are in SI units What is the speed ofthe object at time t 200 s A 640 ms B 943 ms C 700 ms D 765 ms E 130 ms Answer B Var 5 3 An object has a position given by I 20 m 300 msti 30 m 200 ms2t2i where all quantities are in SI units What is the magnitude of the acceleration of the object at time t 200 s A 100 ms2 B 000 ms2 C 0522 ms2 D 400 ms2 E 200 ms2 Answer D Var 5 4 The horizontal coordinates of a FrisbeeTM in a strong wind are given by x 12t 4t2 and y 10t 7 3t2 where x andy are in meters and tis in seconds a What is the acceleration of the Frisbee Give a magnitude and a direction measuring angles from the positive x direction b What is the magnitude of the velocity at t 20 s accurate to the nearest ms Answer a 10 ms2 3230 b 4 ms Var 1 5 An electron moves with a constant horizontal velocity of 30 X 106 ms and no initial vertical velocity as it enters a de ector inside a TV tube The electron strikes the screen after traveling 170 cm horizontally and 400 cm vertically upward with no horizontal acceleration What is the constant vertical acceleration provided by the de ector The effects of gravity can be ignored A 25 x 1014 ms2 B 83 x 102 ms2 C 14 x 104 ms2 D 12 x 1014 ms2 Answer A Var 50 6 A hockey puck slides off the edge of a table at pointA with an initial velocity of 200 ms and experiences no air resistance The height of the tabletop above the ground is 200 m a What is the speed not the velocity of the puck just before it touches the ground b What is the distance between pointA and the point where the puck hits the ground Answer a 210 ms b 129 m Var 1 7 A hockey puck slides off the edge of a table with an initial velocity of 280 ms and experiences no air resistance The height of the tabletop above the ground is 200 In What is the angle below the horizontal of the velocity of the puck just before it hits the ground A 7720 B 7260 C 1280 D 1260 E 3180 Answer D Var 6 8 A boy throws a rock with an initial velocity of 215 ms at 3000 above the horizontal If air resistance is negligible how long does it take for the rock to reach the maximum height of its trajectory A 0110 s B 0194 s C 0215 s D 0303 s Answer A Var 50 9 What is the maximum distance we can shoot a dart from ground level provided our toy dart gun gives a maximum initial velocity of 278 ms and air resistance is negligible A 0789 m B 158 m C 139 m D 0394 m Answer A Var 50 10 A catapult is tested by Roman legionnaires They tabulate the results in a papyrus and 2000 years later the archaeological team reads distances translated into modern units Range 020 km angle of launch 714 landing height launch height What is the initial velocity of launch of the boulders if air resistance is negligible A 44 ms B 14 ms C 22 ms D 069 ms Answer A Var 20 11 A hobby rocket reaches a height of 723 m and lands 111 m from the launch point with no air resistance What was the angle of launch A 6900 B 6740 C 2260 D 4480 Answer A Var 50 12 A ball is thrown at a 6000 angle above the horizontal across level ground It is thrown from a height of 200 m above the ground with a speed of 200 ms and experiences no appreciable air resistance The time the ball remains in the air before striking the ground is closest to A 162 s B 307 s C 332 s D 353 s E 364 s Answer E Var 5 13 A rock is thrown at a window that is located 180 In above the ground The rock is thrown at an angle of 4000 above horizontal The rock is thrown from a height of 200 m above the ground with a speed of 300 ms and experiences no appreciable air resistance If the rock strikes the window on its upward trajectory from what horizontal distance from the window was it released A 532 In B 487 m C 716 m D 298 m E 273 m Answer E Var 1 14 An airplane is ying at a speed of 200 102 ms in level ight at an altitude of 800 102 In A package is to be dropped from the airplane to land on a target on the ground Ignore air resistance a At what horizontal distance away from the target should the package be released so that it lands on the target b In what direction relative to the horizontal will the package be traveling when it hits the ground Answer a 256 km b 3210 below the horizontal Var 1 15 A child throws a ball with an initial speed of 800 ms at an angle of 4000 above the horizontal The ball leaves her hand 100 m above the ground and experience negligible air resistance a How far from where the child is standing does the ball hit the ground b How long is the ball in ight before it hits the ground Answer a 746 m b 122 s Var 1 16 A child throws a ball with an initial speed of 800 ms at an angle of 4000 above the horizontal The ball leaves her hand 100 m above the ground and experience negligible air resistance a What is the magnitude of the ball39s velocity just before it hits the ground b At what angle below the horizontal does the ball approach the ground Answer a 914 ms b 4790 Var 1 17 A projectile is red from point 0 at the edge of a cliff with initial velocity components of vox 60 ms and voy 175 ms as shown in the gure The projectile rises and then falls into the sea at point P The time of ight of the projectile is 400 s and it experiences no appreciable air resistance in ight What is the magnitude of the velocity of the projectile 210 s after it is red v0 y M 77777 gt 0 X Answer 674 ms Var l 18 A projectile is red from point 0 at the edge of a cliff with initial velocity components of vox 600 ms and voy 175 ms as shown in the gure The projectile rises and then falls into the sea at point P The time of ight of the projectile is 400 s and it experiences no appreciable air resistance in ight What is the height of the cliff v0 y M 77777 gt 0 X Answer 840 m Var l 19 A h1ker chff 25 0 rns duected at40 0 wrth the face ofthe cuff as shown 1n the gure The stone hrts the ground 3 75 s atter bemg thrown and feels no appreerab1e an resrstanee as rt falls a Whatrs the herght othe ehm b How far from the foot ofthe chff does the stone land7 e How fast 15 the stone movmg just before rt hrts the gound7 G1 mud Answer a141m b so 3 rn e 58 2 rns Var 1 h m Anuu n u travels m h n m 11 V speed7 Answer 274ms Var 1 1 r t t t n s honzonta1 whatrs the ve1oerty atterthe stam A 66 rns at17 be1ow the horrzonta1 D 80 rns at 37 above the honzontal Answer A Var 1 22 A rescue plane ying horizontally at 726 ms spots a survivor in the ocean 182 m directly below and releases an emergency kit with a parachute Because of the shape of the parachute it experiences insigni cant horizontal air resistance If the kit descends with a constant vertical acceleration of 582 ms2 how far away from the survivor will it hit the waves A 574 m B 454 km C 406 m D 602 m Answer A Var 50 23 An airplane ies between two points on the ground that are 500 km apart The destination is directly north of the origination of the ight The plane ies with an air speed of 120 ms If a constant wind blows at 100 ms due west during the ight what direction must the plane y relative to north to arrive at the destination A 4780 east ofnorth B 4760 east of north C 8520 west ofnorth D 4780 west of north E 4 760 west of north Answer A Var l 24 A plane has an eastward heading at a speed of 156 ms relative to the air A 200 ms wind is blowing southward while the plane is ying The velocity of the plane relative to the ground is A 157 ms at an angle 731O south of east B 157 ms at an angle 731O east of south C 155 ms at an angle 736O south of east D 155 ms at an angle 736O east of south E 157 ms at an angle 736O south of east Answer A Var l 25 A swimmer heading directly across a river 200 m wide reaches the opposite bank in 6 min 40 s during which time she is swept downstream 480 m a How fast can she swim in still water b What is the speed of the current Answer a 050 ms b 12 ms Var l 26 A small boat is moving at a velocity of 335 ms when it is accelerated by a river current perpendicular to the initial direction of motion If the acceleration of the current is 0750 ms2 what will be the new velocity ofthe boat after 335 s A 253 ms at 824 from initial direction of motion B 253 ms at 759 from initial direction of motion C 6401 ms at 824 from initial direction of motion D 6401 ms at 759 from initial direction of motion Answer A Var 50 27 You want to swim straight across a river that is 76 m wide You nd that you can do this if you swim at an angle of 9 28 from the upstream direction at a constant rate of 15 ms relative to the water At what rate does the river ow The angle 9 is measured from the river bank directly upstream is 9 0 while directly across the river is 9 90 A 13 ms B 070 ms C 16 ms D 18 ms Answer A Var 14 28 A longdistance swimmer is able to swim through still water at 40 kmh She wishes to try to swim from Port Angeles Washington directly north to Victoria British Columbia a distance of 50 km An ocean current ows through the Strait of Juan de Fuca from west to east at 30 kmh In what direction relative to north should she swim to make the crossing along a straight line between the two cities A 37 west of north B 37 east of north C 41 west of north D 41 east ofnorth E 49 west of north Answer E Var 1 29 A plane ies directly between two cities A and B which are separated by 2300 mi FromA to B the plane ies into a 65 mih headwind On the return trip from B to A the wind velocity is unchanged The trip from B to A takes 65 min less than the trip fromA to B What is the airspeed of the plane assuming it is the same in both directions A 530 mih B 400 mih C 480 mih D 610 mih Answer A Var 31 30 A cart is moving with a constant horizontal velocity of 500 ms A small pebble is launched from the front of the cart with a velocity of 800 ms at 6000 above the horizontal as measured relative to the cart see gure and experiences no signi cant air resistance Just as the pebble returns to the level from which it was launched its distance from the front of the cart is closest to A 283 m B 460 m C 566 m D 919 m E 113 m Answer C Var 1 31 A ball is tied to the end ofa cable ofnegligible mass The ball is spun in a circle with a radius 200 m making 700 revolutions every 100 seconds What is the magnitude of the acceleration of the ball A 679 ms2 B 387 ms2 C 293 ms2 D 148 ms2 E 742 ms2 Answer B Var 1 32 An electrical motor spins at a constant 28570 revmin If the armature radius is 2685 cm what is the acceleration of the outer edge of the armature A 2403 ms2 B 8444 ms2 C 241100 ms2 D 8440 ms2 Answer A Var 50 33 A satellite orbits the earth a distance of 150 X 107 m above the planet s surface and takes 865 hours for each revolution about the earth The earth39s radius is 638 X 106 m The acceleration of this satellite is closest to A 00690 ms2 B 0870 ms2 C 191 ms2 D 272 ms2 E 980 ms2 Answer B Var l 34 An aircraft performs a maneuver called an quotaileron rollquot During this maneuver the plane turns like a screw as it maintains a straight ight path which sets the wings in circular motion If it takes it 35 s to complete the circle and the wingspan of the plane is 11 In what is the acceleration of the wing tip A 018 ms2 B 099 ms2 C 56 ms2 D 10 ms2 Answer A Var 50 35 An object moves in a circle of radius R at constant speed with a period T If you want to change only the period in order to cut the object s acceleration in half the new period should be A T4 B T2 C T D E 4T Answer D Var l 36 A wind farm generator uses a twobladed propeller see figure mounted on a pylon at a height of 20 m The length of each propeller blade is 12 m A small piece from the tip of the propeller breaks off when the propeller is vertical At that instant the period of the motion of the propeller is 12 s The fragment flies off horizontally falls with negligible air resistance and strikes the ground at P a How far is point P from the base of the pylon b At what angle with respect to the vertical is the fragment moving just as it strikes the ground at P 1 0 12m Answer a 160 m b 68 Var 1 37 A diskshaped space station 175 m in diameter spins uniformly about an aXis perpendicular to the plane of the disk through its center How many rpm revmin must this disk make so that the acceleration of all points on its rim is g2 Answer 226 revmin Var 1 38 Two particles A and B are in uniform circular motion about a common center The acceleration of particle A is 85 times that of particle B The period of particle B is 20 times the period of particle A The ratio of the radius of the motion of particle A to that of particle B is closest to A rArB 21 B rArB 43 C rArB 18 D rArB 024 E rArB 17 Answer A Var 50 University Physics 132 Y oungFreedman Chapter 8 Momentum Impulse and Collisions 81 Conceptual Questions 1 Consider two lessthandesirable options In the first you are driving 30 mph and crash head on into an identical car also going 30 mph In the second option you are driving 30 mph and crash headon into a stationary brick wall In neither case does your car bounce off the thing it hits and the collision time is the same in both cases Which of these two situations would result in the greatest impact force A hitting the other car B hitting the brick wall C The force would be the same in both cases D We cannot answer this question without more information E None ofthese is true Answer C Var l 2 As a tile falls from the roof of a building to the ground its momentum is conserved 3 You are standing on a skateboard initially at rest A friend throws a very heavy ball towards you You can either catch the object or de ect the object back towards your friend such that it moves away from you with the same speed as it was originally thrown What should you do in order to MINIMIZE your speed on the skateboard A Catch the ball B De ect the ball C Your nal speed on the skateboard will be the same regardless whether you catch the ball or de ect the ball Answer A Var l 4 On a smooth horizontal oor an object slides into a spring which is attached to another mass that is initially stationary When the spring is most compressed both objects are moving at the same speed Ignoring friction what is conserved during this interaction A momentum and mechanical energy B momentum only C kinetic energy only D momentum and kinetic energy E momentum and potential energy Answer A Var l 5 A baseball is thrown vertically upward and feels no air resistance As it is rising A both its momentum and its mechanical energy are conserved B its momentum is not conserved but its mechanical energy is conserved C both its momentum and its kinetic energy are conserved D its kinetic energy is conserved but its momentum is not conserved E its gravitational potential energy is not conserved buts its momentum is conserved Answer B Var l 6 A small glider is coasting horizontally when suddenly a very heavy piece of cargo falls out of the bottom of the plane You can neglect air resistance Just after the cargo has fallen out A the plane speeds up and the cargo slows down B the plane speeds up but the cargo does not change speed C neither the cargo nor the plane change speed D the cargo slows down but the plane does not change speed E both the cargo and the plane speed up Answer C Var l 7 A small car has a headon collision with a large truck Which of the following statements concerning the magnitude of the average force due to the collision is correct A The truck experiences the greater average force B The small car experiences the greater average force C The small car and the truck experience the same average force D It is impossible to tell since the masses are not given E It is impossible to tell since the velocities are not given Answer C Var l 8 In a collision between two objects having unequal masses how does magnitude of the impulse imparted to the lighter object by the heavier one compare with the magnitude of the impulse imparted to the heavier object by the lighter one A The lighter object receives a larger impulse B The heavier object receives a larger impulse C Both objects receive the same impulse D The answer depends on the ratio of the masses E The answer depends on the ratio of the speeds Answer C Var l 9 In a perfectly ELASTIC collision between two perfectly rigid objects A the momentum of each object is conserved B the kinetic energy of each object is conserved C the momentum of the system is conserved but the kinetic energy of the system is not conserved D both the momentum and the kinetic energy of the system are conserved E the kinetic energy of the system is conserved but the momentum of the system is not conserved Answer D Var l 10 In an INELASTIC collision between two objects A the momentum of each object is conserved B the kinetic energy of each object is conserved C the momentum of the system is conserved but the kinetic energy of the system is not conserved D both the momentum and the kinetic energy of the system are conserved E the kinetic energy of the system is conserved but the momentum of the system is not conserved Answer C Var 1 11 A shell explodes into two fragments one fragment 25 times heavier than the other If any gas from the explosion has negligible mass then A the momentum change of the lighter fragment is 25 times as great as the momentum change of the heavier fragment B the momentum change of the heavier fragment is 25 times as great as the momentum change of the lighter fragment C the momentum change of the lighter fragment is exactly the same as the momentum change of the heavier fragment D the kinetic energy change of the heavier fragment is 25 times as great as the kinetic energy change of the lighter fragment E the kinetic energy change of the lighter fragment is 25 times as great as the kinetic energy change of the heavier fragment Answer C Var l 12 Jacques and George meet in the middle of a lake while paddling in their canoes They come to a complete stop and talk for a while When they are ready to leave Jacques pushes George s canoe with a force F to separate the two canoes What is correct to say about the nal momentum and kinetic energy of the system if we can neglect any resistance due to the water A The nal momentum is in the direction of F but the final kinetic energy is zero gt B The nal momentum is in the direction opposite of F but the nal kinetic energy is zero C The nal momentum is in the direction of 77 and the nal kinetic energy is positive D The nal momentum is zero and the nal kinetic energy is zero E The nal momentum is zero but the nal kinetic energy is positive Answer B Var l 13 A l0kg block and a 20kg block are pressed together on a horizontal frictionless surface with a compressed very light spring between them They are not attached to the spring After they are released and have both moved free of the spring A the lighter block will have more kinetic energy than the heavier block B the heavier block will have more kinetic energy than the lighter block C both blocks will both have the same amount of kinetic energy D both blocks will have equal speeds E the magnitude of the momentum of the heavier block will be greater than the magnitude of the momentum of the lighter block Answer A Var l 14 There must be equal amounts of mass on both side of the center of mass of an object A True B False Answer B Var l 82 Problems 1 A timevarying horizontal force Ft At4 Bt2 acts for 0500 s on a l225kg object starting at time t 100 s In the SI systemA has the numerical value 450 and B has the numerical value 875 a What are the SI units of A and B b What impulse does this force impart to the object Answer aA Ns4 kg ms6 B Ns2 kg ms4 b 129 N s horizontally Var l 2 A 250kg stone is dropped from rest at a height of 375 In What impulse does gravity impart to this stone from the instant it is dropped until it hits the ground assuming negligible air resistance Answer 214 N s Var l 3 A recracker breaks up into several pieces one of which has a mass of 200 g and ies off along the xaXis with a speed of 820 ms A second piece has a mass of 300 g and ies off along the yaXis with a speed of 450 ms What are the magnitude and direction of the total momentum ofthese two pieces A 361 kgms at 5630 from the x aXis B 935 kgms at 2880 from the xaXis C 212 kgms at 3950 from the xaXis D 361 kgms at 09830 from the xaXis E 212 kgms at 5630 from the xaXis Answer C Var 1 4 A stationary 167kg object is struck by a stick The object experiences a horizontal force given by F at btz where t is the time in milliseconds from the instant the stick rst contacts the object Ifa 1500 Nms and b 20 Nms2 what is the speed ofthe objectjust after it comes away from the stick at t 274 ms A 33 ms B 22 ms C 37 ms D 25 ms Answer A Var 1 5 During a collision with a wall the velocity of a 0200kg ball changes from 200 ms toward the wall to 120 ms away from the wall If the time the ball was in contact with the wall was 600 ms what was the magnitude of the average force applied to the ball A 400 N B 107 N C 167 N D 267 N E 133 N Answer B Var 1 6 A 0500kg ball traveling horizontally on a frictionless surface approaches a very massive stone at 200 ms perpendicular to wall and rebounds with 700 of its initial kinetic energy What is the magnitude of the change in momentum of the stone A 184 kgms B 140 kgms C 300 kgms D 163 kgms E 0000 kgms Answer A Var 5 7 A 620g object traveling at 21 ms collides headon with a 320g object traveling in the opposite direction at 38 ms Ifthe collision is perfectly elastic what is the change in the kinetic energy ofthe 620g object A It loses 023 J B It gains 069 J C It loses 047 J D It loses 14 J E It doesn t lose any kinetic energy because the collision is elastic Answer A Var 1 8 A 23kg object traveling at 61 ms collides headon with a 35kg object traveling in the opposite direction at 48 ms Ifthe collision is perfectly elastic what is the nal speed of the 23kg object A 048 ms B 71 ms C 38 ms D 43 ms E 66 ms Answer B Var 1 9 A car ofmass 1689 kg collides headon with a parked truck of mass 2000 kg Spring mounted bumpers ensure that the collision is essentially elastic If the velocity of the truck is 17 kmh in the same direction as the car39s initial velocity after the collision what was the initial speed of the car A 19 kmh B 38 kmh C 29 kmh D 10 kmh Answer A Var 50 m t rth eoursron the In the gure 0 200 s e1osest to V n n v m M m M Berore After A 19m B185N C 176N D 168N E 160N Answer A Var 1 m bxlhard ball mmally atrest on the level table The mmally rnowng brurard ball de eets 30 0 rorn rts ongmal ddrecnon Whatrs the speed ofthe mmally statronary brurard ball a erthe collxsxon7 A 2 00 rns B 0 866 rns C 1 so rns D 2 59 rns E 0 750 rns Answer c Varl the en speed e ball of4 82 rns After the collxsxon the new speed ofthe eue ball and the relatrve ddrecuon of the balls are 1o e sest A 2 79 rns at 90 to each other B 2 79 rns at oo to each other C 8 34 rns at 90 to each other D 8 34 rns at oo to each other Answer A Varl 13 A 481mg car moving at14 4 ms has from behmd a 571mg carmovmg at13 3 ms 1h the same duecuon 1 the hew speed ofthe heavxer cans 14 0 mswhat15 the speed ofthe hghter small 14 A 10 0 ms A erthe colhsxon the 2 00ng objecthas avelomty 5 00 ms to the west How mueh lunatic energy was lost duhhg the colhsxor A 0 000 I 35161 15 A see the gure 1 The 1mm lunatic energy of the bulletxs e1osest to fv 16 Two objects of the same mass move along the same line in opposite directions The rst mass is moving with speed v The objects collide stick together and move with speed 0100v in the direction of the velocity of the first mass before the collision What was the speed of the second mass before the collision A 120v B 100v C 0900v D 0800v E 000v Answer D Var 1 17 An 80g bullet is shot into a 40kg block at rest on a frictionless horizontal surface see the figure The bullet remains lodged in the block The block moves into an ideal massless spring and compresses it by 87 cm The spring constant of the spring is 2400 Nm The initial velocity of the bullet is closest to V quot k 40 39 Hm kg W A 1100 ms B 1200 ms C 900 ms D 1300 ms E 1000 ms Answer A Var 1 18 In the figure determine the character of the collision The masses of the blocks and the velocities before and after are given The collision is 18 11115 02 ms 06 1115 14 ms Before After A perfectly elastic B partially inelastic C completely inelastic D characterized by an increase in kinetic energy E not possible because momentum is not conserved Answer A Var 1 19 In the gure determan the character of the eolhsron The masses ofthe bloeks andthe Velocmes before and after are grven and no other unbalanced forees act on these bloeks The eolhsron 15 21 ms 0 0 ms 15 1115 15 ms Befmc After A perfeeuy slash E pamally rnelasne C completely melasuc D charact E not p0 Answer enzed by an mcrease m lunatic energy ssrble because momentum 15 not conserved E Var 1 1 507 20 A peed of 12 0 ms 5 8 50 ms and the ball swmgs to amaxlmum hexghth above us ongnal level The value ofh 15 closest to 21 A IUUUrkg car approaches an mtersechon travelmg noth at 20 0 ms A 120mg car eo1hsron whahs the velomty ofthe ears 1mmedAately a er the eo1hsron7 A 29 7 ms m a dArecuon 47 7 east ofnonh B211msm a dArecnon 47 7 west of C151msm a dArecnon 52 8 east ofn D 21 1ms m a dArecuon 52 8 east ofn E 21 1ms m a dArecnon 47 7 east ofnonh s ouLh onh onh An Var 1 22 Two automobiles traveling at right angles to each other collide and stick together CarA has a mass of 1200 kg and had a speed of 25 ms before the collision CarB has a mass of 1600 kg The skid marks show that immediately after the collision the wreckage was moving in a direction making an angle of 400 with the original direction of carA What was the speed of car B before the collision assuming that any other unbalanced forces are negligible A 16 ms B 18 ms C 11 ms D 21 ms E 14 ms Answer A Var 1 23 A 900kg car traveling east at 150 ms collides with a 750kg car traveling north at 200 ms The cars stick together Assume that any other unbalanced forces are negligible a What is the speed of the wreckage just after the collision b In what direction does the wreckage move just after the collision Answer a 122 ms b 4800 N ofE Var 1 24 A car heading north collides at an intersection with a truck of the same mass as the car heading east If they lock together and travel at 28 ms at 460 north of east just after the collision how fast was the car initially traveling Assume that any other unbalanced forces are negligible A 40 ms B 20 ms C 80 ms D 30 ms Answer A Var 41 25 Two ice skaters push off against one another starting from a stationary position The 450kg skater acquires a speed of 0375 ms What speed does the 600kg skater acquire Assume that any other unbalanced forces during the collision are negligible A 0500 ms B 0281 ms C 0375 ms D 0750 ms E 0000 ms Answer B Var 1 26 On a frictionless horizontal table two blocks A of mass 200 kg and B of mass 300 kg are pressed together against an ideal massless spring that stores 750 J of elastic potential energy The blocks are not attached to the spring and are free to move free of it once they are released from rest The maximum speed achieved by each block is closest to A 671 ms A 447 ms B B 447 ms A 671 ms B C 548 ms for both D 612 ms A 500 ms B E 500 ms A 612 ms B Answer A Var 1 27 A 100kg shell is traveling horizontally to the right at 250 ms relative to the ground when it explodes into two fragments one of mass 300 kg and the other of mass 700 kg The lighter fragment goes directly forward and the explosion releases 150 X 103 J of mechanical energy to the fragments Find the magnitude and direction of the velocity of the heavier fragment relative to the ground just after the explosion Ignore the effect of any ejected gases Answer 137 ms to the right Var 1 28 A plate falls vertically to the oor and breaks up into three pieces which slide along the oor Immediately after the impact a 320g piece moves along the xaxis with a speed of 200 ms and a 355g piece moves along the yaxis with a speed of 150 ms The third piece has a mass of 100 g In what direction does the third piece move You can neglect any horizontal forces during the crash A 21690 from the xaxis B 21980 from the xaxis C 3690 from the xaxis D 3990 from the xaxis E 3980 from the xaxis Answer B Var 5 29 A 12kg springactivated toy bomb slides on a smooth surface along the xaxis with a speed of 050 ms At the origin 0 the bomb explodes into two fragments Fragment 1 has a mass of 040 kg and a speed of 090 ms along the negative yaxis Inthe figure the angle 0 made by the velocity vector of fragment 2 and the xaxis is closest to y y y Z 2 Q 080 kg 050 Ins O gt quot9 I r I I 1 Before After E 15 x 12 kg A 31 B 37 C 38 D 53 E 59 Answer A Var l 30 A 12kg springactivated toy bomb slides on a smooth surface along the xaxis with a speed of 050 ms At the origin 0 the bomb explodes into two fragments Fragment 1 has amass of 040 kg and a speed of 090 ms along the negative yaxis In the figure the energy released by the explosion is closest to 1 v v quot quot2 lbeo kg o U l r I 040 kE Bctore A el 090 quot15 A 020 J B 024 J C 028 J D 032 J E 036 J Answer D Var 1 3 l A 200m rod of negligible mass connects two very small objects at its ends The mass of one object is 100 kg and the mass of the other is unknown The center of mass of this system is on the rod a distance 160 In from the 100kg mass object What is the mass ofthe other object A 411 kg B 322 kg C 400 kg D 0250 kg E 0800 kg Answer C Var 5 32 A uniform piece of wire 20 cm long is bent in a right angle in the center to give it an L shape How far from the bend is the center of mass of the bent wire A 25 cm B 35 cm C 45 cm D 50 cm E 71 cm Answer B Var l 33 A long thin rod of lengthL has a linear density lx Ax where x is the distance from the left end of the rod a How far is the center of mass of the rod from the left end of the rod b What is the mass of the rod Answer a 2L3 b AL22 Var l 34 In the gure four point masses are placed as shown The x and y coordinates of the center of mass are closest to UK 30 m 20 m 20 40 k1 31m I 4 kg 50 kg I 31 H1 2 0 20 kg 39 m 0 20 m 30 m T A 22 m 26 In B 22 In 27 In C 23 m 26 In D 23 m 27 In E 23 m 28 m Answer E Var l 35 In the gure a 60cm length of uniform wire of 60 g mass and negligible thickness is bent into a right triangle The x and y coordinates of the center of mass in cm are closest to VV 26 cm JO cm 0 24 cm 39 A 8 3 B 8 5 C 9 4 D 10 3 E 10 5 Answer D Var 1 36 A 310g air track cart is traveling at 125 ms and a 260g cart traveling in the opposite direction at 133 ms What is the speed ofthe center of mass ofthe two carts A 280 ms B 00732 ms C 0131 ms D 147 ms E 129 ms Answer B Var 5 University Physics 132 Y oungFreedman Chapter 14 Periodic Motion 141 Conceptual Questions 1 The position x of an object varies with time t For which of the following equations relating x and t is the motion of the object simple harmonic motion There may be more than one correct choice A x 5 sin23t Bx8cos 3t Cx4tan2t Dx5sin3t E x 2 cos3t 1 Answer B D E Var l 2 A restoring force of magnitude F acts on a system with a displacement of magnitude x In which of the following cases will the system undergo simple harmonic motion AF 0C J B F 0C sin x C F 0C x2 D F 0C x E F lt7 lx Answer D Var l 3 An object is executing simple harmonic motion What is true about the acceleration of this object There may be more than one correct choice A The acceleration is a maximum when the displacement of the object is a maximum B The acceleration is a maximum when the speed of the object is a maximum C The acceleration is a maximum when the displacement of the object is zero D The acceleration is zero when the speed of the object is a maximum E The acceleration is a maximum when the object is instantaneously at rest Answer A D E Var l 4 The simple harmonic motion of an object is described by the graph shown in the gure What is the equation for the position xt of the object as a function of time t A xt 40 msin27180 st 7130 B xt 40 mcos27180 st 27130 C xt 40 mcos27180 st 7130 D xt 40 mcos27180 st 7130 E xt 80 mcos27180 st 7130 Answer D Var l 5 Which of following graphs describes simple periodic motion with amplitude 200 cm and angular frequency 200 rads A Answer B Var l 6 A mass M is attached to an ideal massless spring When this system is set in motion with amplitude A it has a period T What is the period if the amplitude of the motion is increased to 2A A 2T B T 2 C 5 T D 4T E T Answer E Var l 7 A mass M is attached to an ideal massless spring When this system is set in motion it has a period T What is the period if the mass is doubled to 2M A 2T B T 2 C 5 T D 4T E T Answer C Var l 8 In simple harmonic motion the speed is greatest at that point in the cycle when A the magnitude of the acceleration is a maximum B the displacement is a maximum C the magnitude of the acceleration is a minimum D the potential energy is a maximum E the kinetic energy is a minimum Answer C Var l 9 Ifwe double only the amplitude of a Vibrating ideal massandspring system the mechanical energy of the system A increases by a factor of 15 B increases by a factor of 2 C increases by a factor of 3 D increases by a factor of 4 E does not change Answer D Var l 10 If we double only the mass of a vibrating ideal massandspring system the mechanical energy of the system A increases by a factor of J2 B increases by a factor of 2 C increases by a factor of 3 D increases by a factor of 4 E does not change Answer E Var 1 11 If we double only the spring constant of a vibrating ideal massandspring system the mechanical energy of the system A increases by a factor of x5 B increases by a factor of 2 C increases by a factor of 3 D increases by a factor of 4 E does not change Answer B Var l 12 An object is attached to a vertical ideal massless spring and bobs up and down between the two extreme points A and B When the kinetic energy of the object is a minimum the object is located A at eitherA or B B midway between A and B C 13 of the distance fromA to B D 14 ofthe distance fromA to B E 1 J2 times the distance fromA to B Answer A Var l 13 A frictionless pendulum released from 65 degrees with the vertical will vibrate with the same frequency as if it were released from 5 degrees with the vertical because the period is independent of the amplitude and mass A True B False Answer B Var l 14 A certain frictionless simple pendulum having a length L and mass M swings with period T If both L andM are doubled what is the new period A 4T B 2T C 5 T D T E T4 Answer C Var l 15 A frictionless pendulum clock on the surface of the earth has a period of 100 s On a distant planet the length of the pendulum must be shortened slightly to have a period of 100 s What is true about the acceleration due to gravity on the distant planet A The gravitational acceleration on the planet is slightly greater than g B The gravitational acceleration on the planet is slightly less than g C The gravitational acceleration on the planet is equal to g D We cannot tell because we do not know the mass of the pendulum Answer B Var 1 16 In designing buildings to be erected in an area prone to earthquakes what relationship should the designer try to achieve between the natural frequency of the building and the typical earthquake frequencies A The natural frequency of the building should be exactly the same as typical earthquake frequencies B The natural frequency of the building should be very different from typical earthquake frequencies C The natural frequency of the building should be almost the same as typical earthquake frequencies but slightly higher D The natural frequency of the building should be almost the same as typical earthquake frequencies but slightly lower Answer B Var 1 142 Problems 1 A sewing machine needle moves up and down in simple harmonic motion with an amplitude of 127 cm and a frequency of 255 Hz a What is the maximum speed of the needle b What is the maximum acceleration of the needle Answer a 203 cms b 326 cms2 Var l 2 An object is undergoing simple harmonic motion with frequency f 97 Hz and an amplitude of0 12 m At t 000 s the object is at x 000 In How long does it take the object to go from x 000 m to x 0048 m Answer 00068 seconds Var 50 3 A simple harmonic oscillator has an amplitude of 350 cm and a maximum speed of 260 cms What is its speed when the displacement is 175 cm A 120 cms B 225 cms C 142 cms D 150 cms E 170 cms Answer B Var 5 4 The position of an object that is oscillating on an ideal spring is given by the equation x 123 cm cos126s1t Attime t 0815 s a how fast is the object moving b what is the magnitude of the acceleration of the object Answer a 133 cms b 101 cms2 Var 1 5 A machine part is vibrating along the x axis in simple harmonic motion with a period of 027 s and a range from the maximum in one direction to the maximum in the other of 30 cm At time t 0 it is at its central position and moving in the x direction What is its position when t 55 s Ax 043 cm Bx 051 cm Cx051 cm Dx 13 cm Ex14 cm Answer E Var 1 6 The x component of the velocity of an object vibrating along the x axis obeys the equation vxt 0445 ms sin254 radst 0223 a What is the amplitude of the motion of this object b What is the maximum acceleration of the vibrating object Answer a 00175 m b 113 ms2 Var 1 7 A 120N object is oscillating in simple harmonic motion at the end of an ideal vertical spring Its vertical positiony as a function oftime t is given byyt 450 cm cos 195 s1t 718 a What is the spring constant of the spring b What is the maximum acceleration of the object c What is the maximum speed that the object reaches d How long does it take the object to go from its highest point to its lowest point Answer a 466 Nm b 171 ms2 c 0878 ms d 0161 s Var 1 8 An object of mass 80 kg is attached to an ideal massless spring and allowed to hang in the Earth39s gravitational eld The spring stretches 36 cm before it reaches its equilibrium position If this system is allowed to oscillate what will be its frequency A 26 Hz B 00045 Hz C 067 Hz D 21 Hz Answer A Var 1 9 An object that weighs 2450 N is attached to an ideal massless spring and undergoes simple ha1monic oscillations with a period of 0640 s What is the spring constant of the spring A 245 Nm B 121 Nm C 241 Nm D 0102 Nm E 0610 Nm Answer C Var 1 10 A 225kg object is attached to a horizontal an ideal massless spring on a frictionless table What should be the spring constant of this spring so that the maximum acceleration of the object will be g when it oscillates with amplitude of 450 cm Answer 490 Nm Var 1 11 A 56 kg bungee jumper jumps off a bridge and undergoes simple harmonic motion Ifthe period of oscillation is 112 s what is the spring constant of the bungee cord assuming it has negligible mass compared to that of the jumper A 176 Nm B 211 Nm C 282 Nm Answer A Var 50 V constants In ande whose opposite ends are xedto Walls as shown m the gure What 5 angularfrequency 0mg oscillahonxfk17 5 mm man 5 0 NW k A I Elm NW A 2 5 rads 190 Nm fmdthe 15 In the gure two massesM16 kg andm 12 8 0 kg are connectedto avery hghtngxd bar and are attachedto an 1dea1 massless spnng ofspnng constant 100 Nm The system 15 set 78 ern rnamrnum the 1 Vl hathll 39 L 1280ekg mass 7 16A 1000 the osmllauons thatresult from ths colhsxon7 s D0424rn1265 EU424m5005 Answer A Var 1 17 A 0 25 kg 1dea1 harmomc osmllatorhas atotal mechamcal energy 0M 0 J Ifthe osmllauon arnpmude 15 20 0 ern whatxs me osmllauon frequency7 4 5 Hz 18 A 050kg object is attached to an ideal massless spring of spring constant 20 Nm along a horizontal frictionless surface The object oscillates in simple ha1monic motion and has a speed of 15 ms at the equilibrium position a What is the amplitude of Vibration b At what location are the kinetic energy and the potential energy of the system the same Answer a 024 m b x 017 m Var 1 19 A 15kg mass attached to an ideal massless spring with a spring constant of 200 Nm oscillates on a horizontal frictionless track At time t 000 s the mass is released from rest at x 100 cm That is the spring is stretched by 100 cm a Find the frequency of the oscillations b Determine the maximum speed of the mass At what point in the motion does the maximum speed occur c What is the maximum acceleration of the mass At what point in the motion does the maximum acceleration occur d Determine the total energy of the oscillating system e Express the displacement x as a function of time t Answer a 058 Hz b 037 ms at the equilibrium position c 13 ms2 at maximum displacement d 010 J e x 010 m cos37t Var 1 20 A 0025kg block on a horizontal frictionless surface is attached to an ideal massless spring whose spring constant is 150 Nm The block is pulled from its equilibrium position at x 000 m to a displacement x 0080 m and is released from rest The block then executes simple ha1monic motion along the horizontal xaxis When the displacement is x 0024 In what is the kinetic energy of the block A 044 J B 041 J C 046 J D 049 J E 052 J Answer A Var 50 21 An object ofmass 68 kg is attached to an ideal massless spring of spring constant 1690 Nm The object is Calculate the maximum speed the object reaches during its motion Answer 55 ms Var 50 22 An object weighing 441 N hangs from a vertical massless ideal spring When set in vertical motion the object obeys the equation yt 620 cm cos274 radst 140 a Find the time for this object to vibrate one complete cycle b What are the maximum speed and maximum acceleration of the object c What is the TOTAL distance the object moves through in one cycle d Find the maximum kinetic energy of the object e What is the spring constant of the spring Answer a 229 s b 0170 ms 0465 ms2 c 248 cm d 00649 J e 338 Nm Var 1 23 A frictionless simple pendulum on Earth has a period of 175 s On Planet Xits period is 214 s What is the acceleration due to gravity on PlanetX Answer 655 ms2 Var 1 24 The angle that a swinging simple pendulum makes with the vertical obeys the equation I 0150 rad cos285 radst 166 a What is the length of the pendulum A 015 m B 083 m C 121 m D 202 m E It cannot be determined from the information given b What is the mass of the swinging bob at the end of the pendulum A 285 kg B 166 kg C 0454 kg D 0150 kg E It cannot be determined from the information given Answer a Cb E Var 1 25 In the gure a 0 24ng ball rs suspended from avery hght stnng 9 79 rn1ong ande pulled shghtly to the left As the ball swrngs wrthout fncuon through the lowest part ofxts rnotron rt 979 m wrtu 024 kg Answer 3 5 s Var 1 00 s the rod shouldthe prvotbe 1oeated7 A 7 98 em V eeonds what rs the moment ofmema othe suek about an suns through the pwot7 2 s Answer 1 Var 50 29 The amplitude ofa lightly damped harmonic oscillator decreases from 600 cm to 400 cm in 100 s What will be the amplitude of the harmonic oscillator after another 100 s passes A 200 cm B 167 cm C 300 cm D 000 cm E 267 cm Answer E Var l 30 A lightly damped harmonic oscillator with a damping force proportional to its speed is oscillating with an amplitude of 0500 cm at time t 0 When I 820 s the amplitude has died down to 0400 cm At what value of I will the oscillations have an amplitude of 0250 cm A 185 s B 205 s C 165 s D 255 s E 513 s Answer D Var 1 31 An ideal massless spring with a spring constant of 200 Nm is attached to an object of 750 g The system has a small amount of damping Ifthe amplitude of the oscillations decreases from 100 mm to 500 mm in 150 s what is the magnitude of the damping constant b A 000693 kgs B 00462 kgs C 000762 kgs D 00100 kgs E 000857 kgs Answer A Var l 32 A 215 kg lightly damped harmonic oscillator has an angular oscillation frequency of 0261 rads Ifthe maximum displacement of 20 m occurs when t 000 s and the damping constant b is 074 kg s what is the obj ect s displacement when t 401 s A 050 m B 043 m C 058 m D 065 m Answer A Var 21 33 A 25 kg object is undergoing lightly damped harmonic oscillations If the maximum displacement of the object from its equilibrium point drops to 13 its original value in 18 s what is the value of the damping constant b A 31 kgs B 34 kgs C 37 kgs D 40 kgs Answer A Var 21 34 A 50kg block is attached to an ideal massless spring whose spring constant is 125 Nm The block is pulled from its equilibrium position at x 000 m to a position at x 0687 m and is released from rest The block then executes lightly damped oscillation along the xaXis and the damping force is proportional to the velocity When the block rst returns to x 000 In its x component of velocity is 20 ms and its x component of acceleration is 56 ms2 a What is the magnitude of the acceleration of the block upon release at x 0687 m b Find the damping constant b Answer a 172 ms2 b 14 kgs Var 1 35 An object ofmass of 20 kg hangs from an ideal massless spring with a spring constant of 50 Nm An oscillating force F 48 N cos30 radst is applied to the object What is the amplitude of the resulting oscillations You can neglect damping A 015 m B 030 m C 16 m D 24 m E 080 m Answer A Var 1 Universig Physics 1312 YnungFreedman Chapter 7 Pntential Energy and Energy Cnnservaunn 71 Conceptual Quesnons 1 1s 1 possxble for a system to have negauve potential energy7 A Yes as long as the lunatic energy 15 posmve B Yes as long as are total energyrs posmve C Yes smce me enoree ofthe zero of potenual energy 15 arbnrary D No beeause me mnene energy ofa system must equal 1ts potential energy E Nob ause thxs would have no pnysrea1 rneanrng Answer Var 1 m 1 1 1 1 1 1 A 1 1 1 1 euryed droppmg quxckly at rst and men levelmg out How does he speedv ofa swrrnrner 1 1 1 1 compares thh V2 27 Av1gtv2 3 Two stones one of mass m and the other of mass 2m are thrown directly upward with the same velocity at the same time from ground level and feel no air resistance Which statement about these stones is true A The heavier stone will go twice as high as the lighter one because it initially had twice as much kinetic energy B Both stones will reach the same height because they initially had the same amount of kinetic energy C At their highest point both stones will have the same gravitational potential energy because they reach the same height D At its highest point the heavier stone will have twice as much gravitational potential energy as the lighter one because it is twice as heavy E The lighter stone will reach its maximum height sooner than the heavier one Answer D Var l 4 Two identical balls are thrown directly upward ball A at speed v and ball B at speed 2v and they feel no air resistance Which statement about these balls is correct A BallB will go twice as high as ballA because it had twice the initial speed B Ball B will go four times as high as ball A because it had four times the initial kinetic energy C The balls will reach the same height because they have the same mass and the same acceleration D At its highest point ball B will have twice as much gravitational potential energy as ballA because it started out moving twice as fast E At their highest point the acceleration of each ball is instantaneously equal to zero because they stop for an instant Answer B Var l 5A HMM r dtb box shdesupa y a box of mass 2m Sllwulh A the hghterbox wru go twree as hrgh up the rhehhe as the heavrerbox box C both boxes wru have the same speedjust as they move free ofthe sphhg D both boxes wru reaeh the same maxrrhurh herght on the rhehhe the hghter box Answer A Var 1 o A HMM r dtb box shdesupa y rhstead eorhpress the spnng a dutance of 2x Smoolh A the box wrn go up the rhehhe twree as hrgh as before Answer B Var 1 7A arm n am boxshdesupa y instead use a spnng nayrng force constant 2k Smoolh A the box wru go up the mclme twice as nrgn as before before D All of the above enorees are correct E None othe above enorees rs cement Answer D Varl 8 When an object rs so1e1y underdne m uence ofconservauve forces the sum ofxts lumen and potential energes does not change A True B False Answer A Var 1 9 A ball drops sorne dutance and gams 30 J ofkmeuc energy DoNOTrgnore auresxstance uen gravitational potential energy dAdLhe ball 1ose7 I 10Aba11 30 T warren r a resxstance How rnuen luneth energy 64de ball gam7 A more than 30 I B enaeuy 30 J C less than 30 J nswer c ar 1 11 Block 1 and block 2 have the same mass m and are released from the top oftwo inclined planes of the same height making 300 and 600 angles with the horizontal direction respectively Ifthe coefficient of friction is the same in both cases which of the blocks is going faster when it reaches the bottom of its respective incline A We must know the actual masses of the blocks to answer B Both blocks have the same speed at the bottom C Block 1 is faster D Block 2 is faster E There is not enough information to answer the question because we do not know the value of the coefficient of kinetic friction Answer D Var l 12 A girl throws a stone from a bridge Consider the following ways she might throw the stone The speed of the stone as it leaves her hand is the same in each case and air resistance is negligible Case A Thrown straight up Case B Thrown straight down Case C Thrown out at an angle of 450 above horizontal Case D Thrown straight out horizontally In which case will the speed of the stone be greatest when it hits the water below A Case A B Case B C Case C D Case D E The speed will be the same in all cases Answer E Var l 13 Which if any of the following statements concerning the work done by a conservative force is NOT true A It can always be expressed as the difference between the initial and final values of a potential energy function B It is independent of the path of the body and depends only on the starting and ending points C When the starting and ending points are the same the total work is zero D All of the above statements are true E None of the above statements are true Answer D Var l 14 A potentral energy funehon for systern 1rs gryen by Um Cx2 3r3 The potenhal energy funehon for systern 215 gyen by U2x 7 A Cx2 8x3 where A 15 a posmve quantrty A The force on the two systems wru be tn opposrte duecuons B The force rs rdentzesd on the two systems D There rs no relanonshrp between the forces on the two systems Answer B Var 1 15 The plotrn the gure shows the potentrs1 energy of apamcle due to the force exerted on rt b w m rn m L L the magnrtude ofthe force on the parnele greatest7 pmettttn Em w Mtmm A pornt x 7 2 Problems mmv1000ms ruhw w h mm gure The blockmoves a dutance ofl 67m down he mclme m ahme interval ofU 80 s and a process7 r1 0 m A811 B1001 whose h w mm W 32 0 sister rs at rest he transfenedto the sprmg 1the spnng constant rs 52 9Ncm7 A 423 J B 4230 kl C 423 kl D 4230 1 Answer A 50 4 A tennis ball bounces on the oor three times If each time it loses 220 of its energy due to heating how high does it rise after the third bounce provided we released it 23 m from the oor A 110 cm B 11 cm C 110 mm D 140 cm Answer A Var 50 5 It requires 60 J ofwork is needed to push a 20kg object from pointA to point B ofthe frictionless ramp as shown in the gure What is the length 3 of the ramp from A to B Ll30 Answer 061 m Var l 6 A 20 g bead slides along a frictionless wire as shown in the figure At pointA the bead is moving to the right but with negligible speed A 100 cm 80 cm Potential Energy 0 B a What is the potential energy of the bead at point A b What is the kinetic energy of the bead at point B c What is the speed ofthe bead at pointB d What is the speed ofthe bead at point C Answer a 20 x 102 J b 20 x 102 J c 44 ms d 20 ms Var l 7 A roller coaster of mass 800 kg is moving with a speed of 200 ms at position A as shown in the gure The vertical height above ground level at positionA is 200 m Neglect friction A 200 m 160 m Potemial Energy 0 a What is the total mechanical energy of the roller coaster at point A b What is the total mechanical energy of the roller coaster at point B c What is the speed of the roller coaster at point B d What is the speed of the roller coaster at point C Answer a 173 X 105 J b 173 X 105 J c 657 ms d 344 ms Var l 8 A mass is pressed against but is not attached to an ideal horizontal spring on a frictionless horizontal surface After being released from rest the mass acquires a maximum speed v and a maximum kinetic energy K If instead the mass initially compresses the spring twice as far A Its maximum speed will be 2v and its maximum kinetic energy will be 2K B Its maximum speed will be 2v and its maximum kinetic energy will be J2 K C Its maximum speed will be Vx2 and its maximum kinetic energy will be 2K D Its maximum speed will be 2v and its maximum kinetic energy will be 4K E Its maximum speed will be 4v and its maximum kinetic energy will be 2K Answer C Var l 9 A 20 kg mass is moving along the xaxis The potential energy curve as a function of position is shown in the figure The kinetic energy of the object at the origin is 12 J The system is conservative and there is no friction 20 40 60 80 100 l miriuu m gt a What will be the kinetic energy at 20 m along the xaxis b What will be the speed ofthe object at 60 m along the xaxis Answer a 24 J b 22 ms Var l 10 An 80m massless rod is loosely pinned to a frictionless pivot at 0 as shown in the gure A very small 40kg ball is attached to the other end of the rod The ball is held at A where the rod makes a 300 angle above the horizontal and is released The ballrod assembly then swings freely with negligible friction in a vertical circle between A and B The tension in the rod when the ball passes through the lowest point at D is closest to A 160 N B 200 N C 120 N D 80 N E 40 N Answer A Var 1 11 In the gure a 40kg ball is on the end of a l6m rope that is fixed at 0 The ball is held at point A with the rope horizontal and is given an initial downward velocity The ball moves through three quarters of a circle with no friction and arrives at B with the rope barely under tension The initial velocity of the ball at point A is closest to B 4 0 kg A O A 40 ms B 56 ms C 63 ms D 69 ms E 79 ms Answer D Var l 12 In the gure a very small toy race car of mass m is released from rest on the looptheloop track If it is released at a height 2R above the oor how high is it above the oor when it leaves the track neglecting friction A 167R B 200R C 150R D 133 R E 125R Answer A Var 1 13 In the gure a 500kg block is moving at 500 ms along a horizontal frictionless surface toward an ideal massless spring that is attached to a wall After the block collides with the spring the spring is compressed a maximum distance of 068 In What is the speed of the block when it has moved so that the spring is compressed to only onehalf of the maximum distance gt 500 ms Answer 43 ms Var l 14 A 600kg person drops from rest a distance of 120 m to a platform of negligible mass supported by an ideal stiff spring of negligible mass The platform drops 600 cm before the person comes to rest What is the spring constant of the spring A 256 x 105 Nm B 392 x 105 Nm C 545 X 104 Nm D 412 x 105 Nm E 883 X 104 Nm Answer D Var 1 15 A springloaded dart gun is used to shoot a dart straight up into the air and the dart reaches a maximum height of 24 meters above its point of release The same dart is shot up a second time from the same gun but this time the spring is compressed only half as far compared to the first shot How far up does the dart go this time Neglect friction and assume the spring is ideal and massless A 60 m B 12 m C 30 m D 48 m Answer A Var 1 16 A block slides down a frictionless inclined ramp Ifthe ramp angle is 17 00 and its length is 300 m find the speed of the block as it reaches the bottom of the ramp assuming it started sliding from rest at the top A 131 ms B 172 ms C 926 ms D 240 ms Answer A Var 50 17 Consider the motion of a 100kg particle that moves with potential energy given by Ux 200 Jmx 400 Jm2x2 Suppose the particle is moving with a speed of 300 ms when it is located at x 100 In What is the speed ofthe object when it is located at x 500 m A 213 ms B 300 ms C 468 ms D 367 ms Answer D Var 1 18 A car on a roller coaster starts at zero speed at an elevation above the ground of 26 m It coasts down a slope and then climbs a hill The top of the hill is at an elevation of 16 In What is the speed of the car at the top of the hill Neglect any frictional effects A 14 ms B 18 ms C 10 ms D 90 ms E 60 ms Answer A Var l 19 A projectile is red from ground level at an angle of 4000 above horizontal at a speed of 300 ms What is the speed of the projectile when it has reached a height equal to 500 of its maximum height A 260 ms B 274 ms C 287 ms D 267 ms E 281 ms Answer D Var l 20 A very small 100g object is attached to one end ofa massless 10cm rod that is pivoted without friction about the opposite end The rod is held vertical with the object at the top and released allowing the rod to swing What is the speed of the object at the instant that the rod is horizontal A 071 ms B 40 ms C 14 ms D 28 ms E 28 ms Answer D Var l 21 A 20kg object is moving without friction along the x aXis The potential energy curve as a function of position is shown in the gure and the system is conservative Ifthe speed of the object at the origin is 40 ms what will be its speed at 70 m along the xaXis A 40 ms B 42 ms C 44 ms D 46 ms E 98 ms Answer B Var l 22 A small the hm A c A mm dofhavmg spnng at maximum elongan on7 m Amum H m L V 00 cans at pomtA You can treat the car as apoan mass Answer 5301th Var 1 25 A r p a umform surface When the shrerreaehes the bottorn of the hr11 her speedrs 30 0 rns a How rnueh workrs done by fncuon as the shrer comes down the hrm 5 Answer ae11ox1041 b553N Var 1 26 A 5 00ng objectmoves e1oekwrse around a 50 0 ern radms erreu1arpath At one locauon V L m n d rs 3 00 rns a aroundthe erre1e7 eonstant whatrs the value oth1s rnagnrtude7 Answer a 717 5 I b 5 57 N Var 1 Tw m R ur speed F 0m 1m 1nr110 andthe rnelrne rs 0 260 how far does the block travel up the rnehne7 Answer 3 72 rn Var 1 10m lams how rnueh Work does fneuon do on thrs object as rt slrdes down the rnehne7 Answer 71901 Var 1 29 Ah 0 804g block s heldm place agamstthe spnng by a 677Nhonzonta1 extremal force see the gure The extremal force he removed and the block s projected thh avelomty v112 ms 7 9 ms at the h n m A A 3 extendmg to E The coef cient ofkmeuc nemh over ths seemh he 0 39 The veloeny ofthe block s v3 14 ms at c The blockmoves on to D where n stops The sphhg echstahc ofthe spnng Ts closestto smumh B rongh 2c E y a 0A137ekg blockxs heldm place agamstthe sphhg by a74eNhonzonta1 extremal force see the gure The extremal force 15 removed and the blockxs projected vmh avelomty v112 ms 7 4 ms the h n m A A 3 extendmg to E The coef ment ofkmeuc nemh over ths secuon 15 0 24 The velomty ofthe blockxs v3 14 ms at c The blockmoves on to D where 11 stops The 1mm compression of the Spnngls closest to v smumh B rongh 2c E y a 31A1867kg blockxs heldm place agamstthe spnng by a 817Nhonzonta1 extremal force see the gure The extremal force 15 removed and the blockxs projected vmh avelomty v112 ms 7 ms at e h n m A A extendmg to E The coef ment ofkjnetn fncuon over 11115 seenon 15 blockxs v3 14 ms at C The bloekmoves on closest to 0 28 The velomty ofthe to D where 1 stops The hexght h ofthe ramp 15 smumh B rongh 2c E y a 32 A 2 5kg box slxdmg on arough honzontal surface has a speed of12 ms when umakes one by omes to amomentaryhalt1s 70 so I makes Contact wnh the spnng unh1 11 e 111 ms 2959117 a Whahs the spnng constant ofthe spnng7 Answer a1040Nm b 041 Var 1 33 The only force acting on an object moving along the x aXis is the conservative force given by Fx 200 Nmx 100 Nm3x3 a What is the change in potential energy when the object moves from x 100 m to x 200 m b What is the change in kinetic energy when the object moves from x 100 m to x 200 m Answer a 675 J b 675 J Var 1 34 A force on an object is given by Fx 200 Nmx 300 Nm3x3 What is a potential energy function Ux for this conservative force Answer Ux 100 Nmx2 0750 Nm3x4 Var 1 35 A force on an object is given by Fx 400 Nmx 200 Nm3x3 What is the change in potential energy in moving from x 100 m to x 200 m A 100 J B 150 J C 100 J D 150 J E 120 J Answer B Var 1 36 A potential energy function is given by Ux 300 Jx 100 Jm2x3 What is the force function F x that is associated with this potential energy function Answer Fx 300 N 300 Nm2x2 Var 1 37 A potential energy function is given by Ux 300 Nmx 100 Nm3x3 At what position or positions is the force equal to zero A V6000 m andV600 m B 000 m V300 mandx3 OO m C 100 m and 100 m D 300 m and 300 m E The force is not zero at any location Answer C Var 1 38 The potential energy for a certain mass moving in one dimension is given by Ux 20 Jm3x3 15 Jm2x2 36 Jmx 23 J Find the locations where the force on the mass is zero A 40 m 50 m B 10 m C 20 m 30 m D 30 m 50 m Answer C Var l 39 A particle experiences a force given by FX a x3 Find the potential eld Ux the particle is in Assume that the zero of potential energy is located at x 0 A Ux ax 994 B Ux ax x4 C Ux 3 x2 D Ux 3 x2 Answer A Var l 40 When a particle is a distance r from the origin its potential energy function is given by the equation Ur kr where k is a constant and r x2 y2 22 a What are the SI units of k b Find a mathematical expression in terms of x y and z for the y component of the force on the particle c If U 300 J when the particle is 200 m from the origin nd the numerical value of the y component ofthe force on this particle when it is at the point l00 m 200 m 300 m ky x2y2z Answer a kg ms2 or Jm or N b Fy c 0802 N Var l University Physics 132 Y oungFreedman Chapter 11 Equilibrium and Elasticity 111 Conceptual Questions 1 If the torque on an object adds up to zero A the forces on it also add up to zero B the object is at rest C the object cannot be turning D the object could be accelerating linearly but it could not be turning E the object could be both turning and accelerating linearly Answer E Var 1 2 A heavy boy and a lightweight girl are balanced on a massless seesaw Ifthey both move forward so that they are onehalf their original distance from the pivot point what will happen to the seesaw Assume that both people are small enough compared to the length of the seesaw to be thought of as point masses A It is impossible to say without knowing the masses B It is impossible to say without knowing the distances C The side the boy is sitting on will tilt downward D Nothing will happen the seesaw will still be balanced E The side the girl is sitting on will tilt downward Answer D Var 1 3 Tensile stress is A the strain per unit length B the same as force C the ratio of the change in length to the original length D the applied force per crosssectional area E the ratio of elastic modulus to strain Answer D Var 1 4 Tensile train is A the ratio of the change in length to the original length B the stress per unit area C the same as force D the applied force per crosssectional area E the ratio of stress to elastic modulus Answer A Var 1 5 Two compressible solids are formed into spheres of the same size The bulk modulus of sphere two is twice as large as the bulk modulus of sphere one You now increase the pressure on both spheres by the same amount As a result of the increased pressure how is the change in volume of sphere two A V2 related to the change in volume of sphere one A V1 A AV2 2AV1 B AV2 4AV1 C vV2 AV1 D AV2 l2AV1 E AV2 l4AV1 Answer D Var l 6 Which one of the following stresses would be most likely to cause a bone to fracture A tensile stress B compressive stress C sheer stress D bulk stress Answer C Var l 7 The graph in the gure shows the force on an object as a function of the elongation caused by that force Which statement about this object is true F orc39c Al Elongation A The object obeys Hooke39s law at all points from A to C B The object obeys Hooke s law at all points from B to C C The object obeys Hooke s law at all points from A to B D The elastic limit occurs at point C E The region of elastic behavior occurs from B to C Answer C Var l 112 Problems 1 A light board 10 m long is supported by two sawhorses one at one edge of the board and a second at the midpoint A small 40N weight is placed between the two sawhorses 30 m from the edge and 20 m from the center What forces are exerted by the sawhorses on the board Answer 16 N at the end and 24 N at the midpoint Var l 2 An 820 kgdiver stands at the edge of a light 500m diVing board which is supported by two narrow pillars 160 m apart as shown in the gure Find the magnitude and direction of the force exerted on the diVing board a by pillarA b by pillar B 500 m I 160 m A B Answer a 171 kN downwards b 251 kN upwards Var l 3 A 200kg uniform plank is supported by the oor at one end and by a vertical rope at the other as shown in the gure A 500kg mass person stands on the plank a distance threefourths of the length plank from the end on the oor a What is the tension in the rope b What is the magnitude of the force that the oor exerts on the plank Answer a 466 N b 220 N Var l 4 A 300kg ba11 rests in a frictionless groove as shown in the gure 45 60 a What is the magnitude of the force that the left side of the groove exerts on the ball b What is the magnitude of the force that the right side of the groove exerts on the ball Answer a 264 N b 215 N Var 1 5 A nonuniform 800 g meterstick balances when the support is placed at the 510cm mark At what location on the meterstick should a 500g tack be placed so that the stick will balance at the 500 cm mark A 160 cm B 670 cm C 660 cm D 350 cm E 340 cm Answer E Var 1 6 A 300kg child sits on one end ofa long uniform beam having a mass of 200 kg and a 400 kg child sits on the other end The beam balances when a fulcrum is placed below the beam a distance 110 m from the 300kg child How long is the beam A 212 m B 198 m C 193 m D 207 m E 220 m Answer B Var 1 7 Inthe figure the horizontal lower arm has a mass of 28 kg and its center of gravity is 12 cm from the elbow joint pivot How much force FM must the vertical extensor muscle in the upper arm exert on the lower arm to hold a 75 kg shot put Shot N put 7 25 cm I quotI i y l l quot r 39 39 1 WM 1 v v39 mum quot v3 i quotElb ow L0 ar v i joint m E 1500 N Answer D Var l 8 A 50m long l2kg uniform ladder rests against a smooth vertical wall with the bottom of the ladder 30 m from the wall The coefficient of static friction between the oor and the ladder is 028 What distance measured along the ladder from the bottom can a 60kg person climb before the ladder starts to slip A 40 m B 37 m C 17 m D 13 m E 33 m Answer C Var l 9 A stepladder consists of two halves hinged at the top and connected by a tie rod that keeps the two halves from spreading apart In this particular instance the two halves are 250 m long the tie rod is connected to the center of each half and is 700 cm long An 800N person stands 35 of the way up the stepladder as shown in the gure Neglecting the weight of the ladder and assuming that the ladder is resting on a smooth floor what is the tension in the tie rod Note To solve this problem you must quotcutquot the ladder in half and consider the equilibrium of forces and torques acting on each half of the ladder A 140 N B 240 N C 280 N D 360 N E 560 N Answer A Var l 10 Two identical ladders are 30 m long and weigh 600 N each They are connected by a hinge at the top and are held together by a horizontal rope 10 m above the smooth oor forming a symmetric quotAquot arrangement The angle between the ladders is 60 and both ladders have their center of gravity at their midpoint What is the tension in the rope A 240 N B 300 N C 220 N D 260 N E 280 N Answer E Var l 11 A 120kg refrigerator 200 m tall and 850 cm wide has its center of mass at its geometrical center You are attempting to slide it along the oor by pushing horizontally on the side of the refrigerator The coefficient of static friction between the oor and the refrigerator is 0300 Depending on where you push the refrigerator may start to tip over before it starts to slide along the oor What is the highest distance above the oor that you can push the refrigerator so that it won t tip before it begins to slide A 0710 m B 100 m C 121 m D 142 m E 163 m Answer D Var 1 12 A child is trying to stack two uniform wooden blocks 12 cm in length so they will protrude as much as possible over the edge of atable without tipping over as shown in the figure What is the maximum possible overhang distance d 12 cm S A 5 cm B 6 cm C 7 cm D 8 cm E 9 cm Answer E Var 1 13 A uniform sign is supported against a wall at point P as shown in the gure If the sign is a square 040 m on a side and its mass is 40 kg what is the magnitude of the horizontal force that the wall atP experiences A 20 N B 000 N C 78 N D 98 N Answer A Var 50 14 A uniform 300kg beam 600 m long is freely pivoted at P as shown in the figure The beam is supported in a horizontal position by a light strut 500 m long which is freely pivoted at Q and is loosely pinned to the beam at R A load of mass is suspended from the end of the beam at S A maximum compression of 23000 N in the strut is permitted due to safety The maximum massM ofthe load is closest to 100m R 300m S quot391 P E A 0 m E 4 Q A 789 kg B 554 kg C 1020 kg D 1090 kg E 1320 kg Answer A Var 1 15 A uniform 300kg beam 600 m long is freely pivoted at P as shown in the gure The beam is supported in a horizontal position by a light strut 500 m long which is freely pivoted at Q and is loosely pinned to the beam at R A load of mass is suspended from the end of the beam at S A maximum compression of 23000 N in the strut is permitted due to safety Under maximum load find the magnitude of the x component of the force exerted on the beam by the pivot at P P 300 R 300m S A 13800 N B 12800 N C 11200 N D 14400 N E 16000 N Answer A Var 1 16 A 100kg uniform ladder that is 250 m long is placed against a smooth vertical wall and reaches to a height of 210 m as shown in the gure The base ofthe ladder rests on a rough horizontal oor whose coefficient of static friction with the ladder is 0800 An 800kg bucket of concrete is suspended from the top rung of the ladder right next to the wall as shown in the figure What is the magnitude of the friction force that the oor exerts on the ladder 210 uS 0800 A 538 N B 706 N C 1290 N D 833 N E 601 N Answer A Var l 17 A dump truck has a large cubical concrete block in its bed The coefficients of friction between this block and the oor ofthe bed are uk 0450 and us 0650 As the bed is slowly tilted above the horizontal will the brick first begin to slide or will it first tip over A It will first tip over B It will first begin to slide C It will tip over just as it begins to slide D It is impossible to answer without knowing the mass of the block E It is impossible to answer without knowing the dimensions of the block Answer B Var l V V gure you observe that the mammum that the angle 9 can be wrthout uppmg over the bnekrs 49 6 bn ck7 8 00 cm e 19 A 20 Mg umform doorhas awrdth of120 m and aherght of2 50 m The doons mounted on apost by aparr ofhmges marked 1 and 2 m the gure at the top and bottom ofthe door An at an angl oo o s shownx efxgure he ob 15 1 mm above the bottom ofthe door a Fmd the x eompoheht ofthe force that hmge 1 exerts on the door at the top b End the SUM ofthey eompouehts of the forces thathmges 1 and 2 together exert on the door 1mm Answer a 753 4 N b 166 N Var 1 20 In the figure a uniform rectangular crate 040 m wide and 10 m tall rests on a horizontal surface The crate weighs 930 N and its center of graVity is at its geometric center A horizontal force F is applied at a distance h above the oor If h 061 m what minimum value of F is required to make the crate start to tip over Static friction is large enough that the crate does not start to slide 040m E T F 10 m T h iw Answer 305 N Var 50 21 In the figure a 100m long bar is attached by a frictionless hinge to a wall and held horizontal by a rope that makes an angle 6 of 53 with the bar The bar is uniform and weighs 399 N How far from the hinge should a 100kg mass be suspended for the tension T in the rope to be 125 N Answer 815 m from the hinge Var 1 22 In the gure aumform ladder 12 meters long rests agamst averueal fncnonless wall The ladder welghs 400 N and makes an angle 50f 79 Wlth the oor A man wergung 790 Ncllmbs e Answer 0 12 Var 50 23 A steel gultar smng wth a dlameter of 0 300 mm and alength of70 0 em ls stretched by Young s modulus for steel ls 2 o gtlt1011Nm2 Answer 10 IN Var l 24 A vemeally A m2 Whatls the elongauon ofthe rod due to ths objec A l 2 em 25 A 0600mm diameter wire stretches 0500 of its length when it is stretched with a tension of 200 N What is the Young39s modulus of this wire A 566 X 1010 Nm2 B 354 X109 Nm2 C 141 x 1010 Nm2 D 643 x 109 Nm2 E 278 x 109 Nm2 Answer C Var l 26 A cable is 100 m long has a crosssectional area of 10 mm2 and is made ofa material having a Young s modulus of 10 X 1011 Nm2 Ifa 1000N force is applied to stretch the cable how far does it stretch A 00010 In B 0010 m C 010 m D 10 m E 10 m Answer D Var l 27 A steel lift column in a service station is a solid cylinder 40 m long and 020 m in diameter Young39s modulus for this steel is 20 X 1010 Nm2 By what distance does the column compress when a 5000kg truck is on it A 47 X 107 m B 80 X 107 m C 32 x 106 m D 78 x 106 m E 31 x 105 m Answer E Var l 28 The tensile strength the maximum tensile stress it can support without breaking for a certain steel wire is 3000 MNm2 What is the maximum load that can be applied to a wire with a diameter of 30 mm made of this steel without breaking the wire A 64 kN B 90 kN C 42 kN D 85 kN E 21 kN Answer E Var l 29 A steel rod 55 cm long has a diameter of 30 cm The compressive strength the maximum stress it can support without breaking of this steel is 500 X 106 Nm2 What is the compression force that would break the rod A 35 X 107 N B 24 x 107 N C 14 x 108 N D 47 x 108 N E 89 x 108 N Answer A Var 1 30 A very light 100m wire consists of two segments of equal length one of steel Young s modulus is 200 X 1011 Nm2 and one of brass Young39s modulus is 90 X 1010 Nm2 The steel segment is 150 mm in diameter and the brass segment has twice this diameter When a weight w is hung from the ceiling by this wire the steel segment stretches by 110 mm Find the weight w A 190 N B 390 N C 780 N D 1000 N E 3100 N Answer C Var 1 31 A very light 100m wire consists oftwo segments of equal length one of steel Young s modulus is 200 X 1011 Nm2 and one of brass Young39s modulus is 90 X 1010 Nm2 The steel segment is 150 mm in diameter and the brass segment has twice this diameter When a weight w is hung from the ceiling by this wire the steel segment stretches by 110 mm By what distance does the brass segment stretch A 050 mm B 061 mm C 12 mm D 24 mm E 98 mm Answer B Var 1 32 What is the maximum length of a metal cable that can hang vertically supported from one end of the cable The Young s modulus of this metal is 210 X 1011 Nm2 its tensile strength the maximum tensile stress it can support without breaking is 740 X 108 Nm2 and its density is 760 x 103 kgm3 A 994 km B 422 km C 456 km D 175 km E 248 km Answer A Var l 33 An aluminum wire and a steel wire each of length 20 m are hung from the ceiling A 50kg mass is suspended from the lower end of each wire The aluminum wire has a diameter of 22 mm What must be the diameter of the steel wire if it is to stretch the same distance as the aluminum wire so that the two wires maintain equal lengths after the masses are attached Young39s modulus for aluminum is 070 X 1011 Nm2 and for steel it is 20 X 1011 Nm2 Answer 13 mm Var l 34 A copper sphere has a radius of 250 m under normal room pressure of 10 X 105 Nm2 If we increase the pressure on this sphere to 10 times the normal room pressure what is the change in its volume The bulk modulus for copper is 14 X 1011 Pa Answer 42 X 10394 m3 Var l 35 A solid steel sphere with a radius of 20 m falls off a ship and sinks to a depth where the pressure is 15 MNm2 The bulk modulus for this steel is 16 X 1011 Nm2 What is the change in the radius of the sphere A 0021 mm B 42 mm C 042 mm D 0 19 mm E 0062 mm Answer E Var l 36 At a depth of about 1030 m in the sea the pressure has increased by 100 atmospheres to 10 X 107 Nm2 By how much has 10 m3 of water been compressed by this pressure The bulk modulus ofwater is 23 X 109 Nm2 A 23 x 103 m3 B 33 x103 m3 C 43 x 103 m3 D 53 X 103 m3 E 63 X 103 m3 Answer C Var 1 37 A 12L volume of oil is subjected to a pressure change which produces a volume strain on the oil of 30 X 104 The bulk modulus ofthe oil is 60 X 109 Nm2 and is independent ofthe pressure By how many milliliters does this pressure reduce the volume of the oil A 20 mL B 24 mL C 28 mL D 32 mL E 36 mL Answer E Var 1 38 A 12L volume of oil is subjected to a pressure change which produces a volume strain on the oil of 30 X 104 The bulk modulus ofthe oil is 60 X 109 Nm2 and is independent ofthe pressure What is the pressure change that produced the volume strain in the oil A 12 MNm2 B 14 MNm2 C 16 MNm2 D 18 MNm2 E 20 MNm2 Answer D Var 1 39 When the pressure applied to an unknown liquid is increased from 10 X 107 Nm2 to 55 X 107 Nm2 the volume of the liquid decreases by 070 Calculate the bulk modulus of the liquid Answer 64 X 109 Nm2 Var 1 40 A shear force of 400 N is applied to one face of an aluminum cube with sides of 30 cm while the opposite face is held fixed in place What is the resulting displacement of the face The shear modulus for aluminum is 25 X 1010 Nm2 A 19 X 108 m B 26 x 108 m C 44 x 108 m D 53 x 108 m E 82 x 108 m Answer D Var 1 41 The base of an aluminum block which is fixed in place measures 90 cm by 90 cm and the height of the block is 60 cm A force applied to the upper face and parallel to it produces a shear strain of 00060 The shear modulus of aluminum is 30 X 1010 Nm2 What is the displacement of the upper face in the direction of the applied force A 30 mm B 36 mm C 42 mm D 48 mm E 54 mm Answer B Var 1 42 The base of an aluminum block which is xed in place measures 90 cm by 90 cm and the height of the block is 60 cm A force applied to the upper face and parallel to it produces a shear strain of 00060 The shear modulus of aluminum is 30 X 1010 Pa What is the sheer stress on the block A 180 X 106 Nm2 B 360 X 106 Nm2 C 600 x 106 Nm2 D 720 x 106 Nm2 E 900 x 106 Nm2 Answer A Var 1 43 A sample of tendon 300 cm long and 400 mm in diameter is found to break under a minimum force of 128 N If instead the sample had been 150 cm long and of uniform composition and crosssectional area what minimum force would have been required to break it A 32 N B 64 N C 128 N D 256 N E 512 N Answer C Var 1 University Physics 132 Y oungFreedman Chapter 5 Applying Newton39s Laws 51 Conceptual Questions 1 A 615 N student standing on a scale in an elevator notices that the scale reads 645 N From this information the student knows that the elevator must be moving A downward B upward C You cannot tell if it is moving upward or downward Answer C Var 1 2 Which one of the following freebody diagrams best represents the freebody diagram with correct relative force magnitudes of a person in an elevator that is traveling upward with an gt unchanging velocity Ff is the force of the oor on the person and F g is the force of gravity on the person gt 3 Which one of the following freebody diagrams best represents the freebody diagram with correct relative force magnitudes of a person in an elevator that is traveling upward but is gt gt gradually slowing down at a rate of 9 ms2 F f is the force of the oor on the person and F g is the force of gravity on the person A 1 03H m 50 m s by averucal pull P The tensxon m the wire 15 Tsee gure Whth one ofthe followmg relationshxps between Tand Pmust be tme7 Pull p Tension T 5 Two objects having masses m1 and m2 are connected to each other as shown in the gure and are released from rest There is no friction on the table surface or in the pulley The masses of the pulley and the string connecting the objects are completely negligible What must be true about the tension T in the string just after the objects are released A T m2g B T gt ng C T lt m2g D T mig E T gt mlg Answer C Var l 6 Two bodies P and Q on a smooth horizontal surface are connected by a light cord The mass gt of P is greater than that of Q A horizontal force F of magnitude F is applied to Q as shown in the gure accelerating the bodies to the right The magnitude of the force exerted by the connecting cord on body P will be F P l l Q l gt Azero B less thanF but not zero C equal to F D greater than F Answer B Var l 7 Two unequal massesM and m M gt m are connected by a light cord passing over a pulley of negligible mass as shown in the gure When released the system accelerates Friction is negligible Which gure below gives the correct freebody force diagrams for the two masses in the moving system A I m Answer C Var l 8 Two objects have masses m and 5m respectively They both are placed side by side on a frictionless inclined plane and allowed to slide down from rest A It takes the lighter object 5 times longer to reach the bottom of the incline than the heaVier object B It takes the lighter object 10 times longer to reach the bottom of the incline than the heaVier object C It takes the heaVier object 5 times longer to reach the bottom of the incline than the lighter object D It takes the heaVier object 10 times longer to reach the bottom of the incline than the lighter object E The two objects reach the bottom of the incline at the same time Answer E Var l 9 A gramtatlonal force on tlne box ls alreeteol A parallel to the plane m tln l n as the movement of e same reet o tlne box opposlte alreeuon as tlne movement ofthe box B parallel to the plane m tlne C perpendlcular to the plane D vemcally E at an angle Sbelowthe melmeol plane Answer D Var l 10 A erate ls shdmg down an melmeolramp at a eonstant speed 0150 55 ms The veetor sum of all tlne forces aeung on tlus erate must pomt down the ramp rue H bnck along the melme ls A zero B equal to tlne Welght ofthe bnck C greater than tlne welgnt ofthe bnck D less tlnan tne welgnt othe bnck Answer D Var We denote cls tlne and How are 13 If you swing a bucket of water fast enough in a vertical circle at the highest point the water does not spill out because an outward force balances the pull of gravity on the water A True B False Answer B Var 1 14 A string is attached to the rearview mirror of a car A ball is hanging at the other end of the string The car is driving around in a circle at a constant speed Which of the following lists gives all of the forces directly acting on the ball A tension and gravity B tension C tension gravity and the centripetal force D tension gravity the centripetal force and friction Answer A Var l 15 Suppose a highway curve is properly banked to eliminate friction for a speed of 45 mph If your tires were bald and you wanted to avoid sliding on the road you would have to drive A somewhat below 45 mph B somewhat above 45 mph C at exactly 45 mph Answer C Var l 16 When a parachutist jumps from an airplane he eventually reaches a constant speed called the terminal speed Once he has reached terminal speed A his acceleration is equal to g B the force of air drag on him is equal to zero C the force of air drag on him is equal to g D his speed is equal to g E the force of air drag on him is equal to his weight Answer E Var l 17 Suppose the force of the air drag on an object is proportional to the speed of the object and in the direction opposite the object s velocity If you throw an object upward the magnitude of its acceleration is greatest A right after the object is released B at the top of its trajectory C The acceleration of the object is the same throughout the entire trajectory Answer A Var l 52 Problems 1 A 600kg person rides in an elevator while standing on a scale The scale reads 400 N The acceleration of the elevator is closest to A 313 ms2 downward B 667 ms2 downward C zero D 980 ms2 downward E 667 ms2 upward Answer A Var l 2 A 600kg person rides in elevator while standing on a scale The elevator is traveling downward but slowing down at a rate of 200 ms2 The reading on the scale is closest to A 589 N B 708 N C 469 N D 120 N E 349 N Answer B Var l 3 Two objects are connected by a very light exible string as shown in the gure where M 060 kg and m 040 kg You can ignore friction and the mass of the pulley a Draw freebody diagrams for each object b Calculate the magnitude of the acceleration of each object c Calculate the tension in the string Answer a The force of gravity acts downward and tension acts upward on each object b 20 ms2 c 47 N Var l 4 Three boxes in contact rest sidebyside on a smooth horizontal oor Their masses are 50 kg 30kg and 20kg with the 30kg box in the center Aforce of 50 N pushes on the 50kg box which pushes against the other two boxes a Draw the freebody diagrams for each of the boxes b What magnitude force does the 30kg box exert on the 50kg box c What magnitude force does the 30kg box exert on the 20kg box Answer a The following forces act on the 50kg box the force due to gravity normal force contact force between 50kg mass and 30kg mass the force of 50 N pushing on the box The following forces act on the 30kg box the force due to gravity normal force contact force between the 50kg box and the 30kg box the contact force between the 30kg box and the 20 kg box The following forces act on the 20kg box the force due to gravity normal force contact force between the 30kg box and the 20kg box b 25 N c 10 N Var l 5 The figure shows a lOOkg block being released from rest from a height of 10 m It then takes it 090 s to reach the oor What is the mass m of the other block The pulley has no appreciable mass or friction A 60 kg B 54 kg C 48 kg D 42 kg Answer A Var 1 6 A wooden blockA of mass 40 kg slides on a frictionless table when pulled using a massless string and pulley array by a hanging box B of mass 50 kg as shown in the gure What is the acceleration of blockA as it slides on the frictionless table Hint Think carefully about the acceleration constraint A 41 ms2 B 35 ms2 C 31 ms2 D 27 ms2 Answer A Var l 7 The figure shows two 10 kgblocks connected by a rope A second rope hangs beneath the lower block Both ropes have a mass of 250 g The entire assembly is accelerated upward at 23 9 ms2 by force F What is the tension at the top end of rope I A 18N B 15 N C 29N D 35 N Answer A Var l 8 A 600kg block is in contact with a 400kg block on a horizontal frictionless surface as shown in the gure The 600kg block is being pushed by a horizontal 200N force as shown What is the magnitude of the force that the 600kg block exerts on the 400kg block kg IIIIII IIIII 2940 600 400 kg A 600 N B 200 N C 800 N D 400 N E 100 N Answer C Var l 9 s are connected by massless wires over a massless frictionless pulley as shown in the gure The tension in the wire connecting the 100kg and 150kg objects is measured to be 133 N What is the mass M b 1500 kg e 133 N 1000 kg A 833 kg B 339 kg C 350 kg D 528 kg E 950 kg Answer D Var l 10 Three objects are connected by massless wires over a massless frictionless pulley as shown in the gure The tension in the wire connecting the 100kg and 150kg objects is measured to be 133 N What is the tension in wire A gt 1500 kg 6 133N 1000 kg A 875 N B 245 N C 280 N D 333 N E 517 N Answer D Var 1 11 A 200N box rests on a 500N box on a perfectly smooth horizontal floor When a horizontal 150N pull to the right is exerted on the lower box see gure both boxes move together Find the magnitude and direction of the net external force on the upper box 200 N 500N 6 150 N pull I Answer 429 N to the right Var 1 12 A block is given a very brief push up a 2000 frictionless incline to give it an initial speed of 120 ms a How far along the surface of the plane does the block slide before coming to rest b How much time does it take to return to its starting position Answer a 215 m b 716 s Var 1 13 A child on a sled starts from rest at the top of a 150 slope If the trip to the bottom takes 152 s how long is the slope Assume that frictional forces may be neglected A 293 m B 586 m C 1130 m D 147 m Answer A Var 50 14 A system comprising blocks a light frictionless pulley a frictionless incline and connecting ropes is shown in the gure The 90kg block accelerates downward when the system is released from rest The tension in the rope connecting the 60kg block and the 4 0kg block is closest to A 30 N B 33 N C 36 N D 39 N E 42 N Answer E Var 1 15 A 500kg box rests on a horizontal surface The coefficient of static friction between the box and the surface is 0300 and the coef cient of kinetic friction is 0200 What is the friction force on the box if a a horizontal l40N push is applied to it b a horizontal l75N push is applied to it Answer a 140 N b 980 N Var l 16 A 400kg block rests between the oor and a 300kg block as shown in the gure The 300kg block is tied to a wall by a horizontal rope Ifthe coefficient of static friction is 0800 between each pair of surfaces in contact what horizontal force F must be applied to the 4 00kg block to make it move 300 kg 400 kg 39gt A 162 N B 549 N C 211 N D 235 N E 784 N Answer E Var 1 17 A 150N box is being pulled horizontally in a wagon accelerating uniformly at 300 ms2 The box does not move relative to the wagon the coefficient of static friction between the box and the wagon s surface is 0600 and the coefficient of kinetic friction is 0400 The friction force on this box is closest to A 450 N B 900 N C 600 N D 459 N Answer D Var 1 18 In a shuf eboard game the puck slides atotal of 12 m before coming to rest If the coefficient of kinetic friction between the puck and the horizontal board is 028 what was the initial speed of the puck A 81 ms B 290 ms C 65 ms D 73 ms Answer A Var 31 19 A driver in a 1000 kg car traveling at 20 ms slams on the brakes and skids to a stop Ifthe coefficient of friction between the tires and the horizontal road is 080 how long will the skid marks be A 26 m B 21 m C 33 m D 24 m Answer A Var 27 20 Jason takes off from rest across level water on his jetpowered skis The combined mass of Jason and his skis is 75 kg the mass ofthe fuel is negligible The skis have athrust of 200 N and a coefficient of kinetic friction on water of0 10 Unfortunately the skis run out of fuel after only 48 s What is Jason s top speed A 81 ms B 130 ms C 13 ms D 48 ms Answer A Var 50 21 Jason takes off from rest across level water on his jetpowered skis The combined mass of Jason and his skis is 75 kg the mass ofthe fuel is negligible The skis have athrust of 200 N and a coefficient of kinetic friction on water of0 10 Unfortunately the skis run out of fuel after only 67 s How far has Jason traveled when he finally coasts to a stop A 10000 m B 7600 m C 5400 m D 3800 m Answer A Var 50 22 Kieran takes off from rest down a 50 m high 100 slope on his jetpowered skis The skis have a thrust of 280 N parallel to the surface of the slope The combined mass of skis and Kieran is 50 kg the fuel mass is negligible Kieran s speed at the bottom is 40 ms What is the coefficient of kinetic friction of his skis on snow A 047 B 058 C 023 D 029 Answer A Var 34 23 A factory robot drops a 10 kg computer onto a conveyor belt running at 31 ms The materials are such that us 050 and uk 030 between the belt and the computer How far is the computer dragged before it is riding smoothly on the belt A 16 m B 098 m C 23 m D 30 m Answer A Var 50 24 You push downward on a box at an angle 250 below the horizontal with a force of 750 N If the box is on a at horizontal surface for which the coefficient of static friction with the box is 076 what is the mass of the heaviest box you will be able to move A 59 kg B 68 kg C 54 kg D 82 kg Answer A Var 31 25 A person is dragging a packing crate of mass 100 kg across a rough horizontal oor where the coefficient of kinetic friction is 0400 He exerts a force F sufficient to accelerate the crate forward At what angle above horizontal should his pulling force be directed in order to achieve the maximum acceleration A 2180 B 2770 C 300 D 3450 E 450 Answer A Var l 26 A packing crate rests on a horizontal surface It is acted on by three horizontal forces 600 N to the left 200 N to the right and friction The weight of the crate is 400 N If the 600N force is removed the resultant force acting on the crate is A zero B 200 N to the right C 200 N to the left D 400 N to the left E impossible to determine from the information given Answer A Var l 27 A pickup truck is moving at 25 ms with a toolbox of mass m resting on the bed ofthe truck 25 m behind the cab Suddenly the brakes are applied causing the toolbox to slide and the truck comes to a stop in 47 s The coefficient of kinetic friction between the toolbox and the bed of the truck is 028 After the brakes are applied how much time elapses before the toolbox strikes the cab Answer 14 s Var l 28 Two boxes are connected by a weightless cord running over a very light frictionless pulley as shown in the figure Box A of mass 80 kg is initially at rest on the top ofthe table The coefficient of kinetic friction between boxA and the table is 010 Box B has a mass of 150 kg and the system begins to move just after it is released A o a Draw the freebody diagrams for each of the boxes identifying all of the forces acting on each one b Calculate the acceleration of each box c What is the tension in the cord Answer a BoxA is acted on by the downward force of gravity the upward normal force due to the table top the tension in the string toward the right and the force of friction due to the table top toward the left Box B is acted on by the downward force of gravity and the upward tension of the string b 61 ms2 c 56 N Var 1 29 A rope pulls on the lower block in the gure with a tension force of 20 N The coefficient of kinetic friction between the lower block and the surface is 016 The coefficient of kinetic friction between the lower block and the upper block is also 016 The pulley has no appreciable mass or friction What is the acceleration of the 20 kg block A 41 ms2 B 51 ms2 C 84 ms2 D 92 ms2 Answer A Var l 30 Three objects are connected as shown in the gure The strings and frictionless pulleys have negligible masses and the coefficient of kinetic friction between the 20kg block and the table is 025 What is the acceleration of the 20kg block 3 kg A 25 ms2 B 17 ms2 C 32 ms2 D 40 ms2 Answer A Var 50 31 A system comprised blocks a light frictionless pulley and connecting ropes is shown in the gure The 90kg block is on a perfectly smooth horizontal table The surfaces of the 12kg block are rough with uk 030 between the block and the table If the 50kg block accelerates downward when it is released find its acceleration A 10 ms2 B 12 ms2 C 14 ms2 D 16 ms2 E 18 ms2 Answer A Var l m A as h quotmm Ram u nerome A A 7 A A 7 30 w m 1 adjusteduntxl 16m52 X7 m m a m V uspendedby H w 0 over the oor 34A L the lowerh the U39PPER box7 400 kg 100 kg Pull 5amp0 N A 19 3Nto Lhanght E 31 4Ntothele Answer A Var 3s A 200 g hockey puckxs launchedup ametal ramp mans mclmed at a 30 angle The anduk 0 30 respectively The puck s mm Speed s 63 ms What vemcal height does the puckreach above its stamng pomt 130 m 37 A 200 g hockey puck is launched up a metal ramp that is inclined at a 300 angle The coefficients of static and kinetic friction between the hockey puck and the metal ramp are us 040 and uk 030 respectively The puck s initial speed is 49 ms What speed does it have when it slides back down to its starting point A 28 ms B 35 ms C 42 ms D 49 ms Answer A Var 50 38 A 400kg block rests on a 3000 incline as shown in the gure Ifthe coefficient of static friction between the block and the incline is 0700 what magnitude horizontal force F must act on the block to start it moving up the incline F A 340 N B 511 N C 547 N D 840 N E 764 N Answer D Var 1 39 A box is sliding down an incline tilted at a 1200 angle above horizontal The box is initially sliding down the incline at a speed of 150 ms The coefficient of kinetic friction between the box and the incline is 0340 How far does the box slide down the incline before coming to rest A 0920 m B 233 m C 178 m D 0720 m E The box does not stop It accelerates down the plane Answer A Var 5 40 A 500kg block is being pulled up a 1600 slope by a force of 250 N which is parallel to the slope The coefficient of kinetic friction between the block and the slope is 0200 What is the magnitude of the acceleration of the block A 0528 ms2 B 0158 ms2 C 0412 ms2 D 0983 ms2 E 0260 ms2 Answer C Var 5 41 Two blocks are connected by a string that goes over an ideal pulley as shown in the gure BlockA has a mass of300 kg and can slide over a rough plane inclined 3000 to the horizontal The coefficient of kinetic friction between blockA and the plane is 0400 BlockB has a mass of 277 kg What is the acceleration of the blocks A 0392 ms2 B 196 ms2 C 312 ms2 D 535 ms2 E 000 ms2 Answer A Var l 42 The gure shows two packages that start sliding down a 20 ramp from rest a distance d 66 m along the ramp from the bottom Package A has a mass of 50 kg and a coef cient of kinetic friction 020 between it and the ramp Package B has a mass of 10 kg and a coef cient of kinetic friction 015 between it and the ramp How long does it take package A to reach the bottom A 27 s B 30 s C 32 s D 35 s Answer A Var 50 43 In the gure a Tbar ski tow pulls a skier up a hill inclined at 10 above horizontal The skier starts from rest and is pulled by a cable that exerts a tension T at an angle of 30 above the surface of the hill The mass of the skier is 60 kg and the effective coef cient of kinetic friction between the skis and the snow is 0100 What is the maximum tension in the cable if the starting acceleration is not to exceed 0400 g T A 246 N B 366 N C 431 N D 187 N E 535 N Answer C Var 1 44 A zsoekg crate 15 on arough ramp mclmed at 30 above the horizontal The coef cient of cratepushmg u up the ramp What 15 the aeeelerauon ofthe crate7 A 8 4 m52 150 ms by averucal pull P The tensxon m the we 15 Tsee gure sz closest to Full 139 Tensxon T N and F2 2 1 N What thud force Will cause the object to be m ethbnum aeeelerauon s 3 equals zero7 2 A 6 6 Nat162 counterclockwxse from I 1 a B s s N at108 counterclockwxse from F1 a C 4 2 N at1s2 counterclockwxse from F1 D 4 2 Nat108 counterclockwxse from 31 Answer A 47 The gure shows two forces each ofmagmtude 4 s N aetmg on an object The angle What tth force wtu cause the objectto be m ethbnum accelerahon equals zero7 I A 8 s Npomtmg to the nght 48 A traf c light weighing 100 N is supported by two ropes as shown in the gure The tensions in the ropes are closest to 37 37 A 50 N B 56 N C 63 N D 66 N E 83 N Answer E Var l 49 Two blocks are connected by a string that goes over an ideal pulley as shown in the gure and pulls on block A parallel to the surface of the plane Block A has a mass of 300 kg and can slide along a rough plane inclined 300 to the horizontal The coef cient of static friction between block A and the plane is 0400 What mass should block B have in order to start block A sliding up the plane Answer 254 kg Var l 29 1800 The rollmg the cable car needle descend at constant speed7 Cnumurwcxgm A 3800 N Hum Rm L L N and makes an angle wath the cexlmg Whats the angle 57 53 A gure ram P wages 650 w that can be usedto holdthxs crate stationary on the mp7 m A ASUVN force The L A K A quotblock 030 mm a m m m 1 A A65kg B72kg C80kg D88kg E95kg Answer A Varl 55 A 23 kg mass 15 connectedto anal on afncuonless table by amassless stnng13 m long mm Mu make one complete revolutxor A 4 8 s 56 A car travels at a steady 400 ms around a horizontal curve of radius 200 In What is the minimum coefficient of static friction between the road and the car39s tires that will allow the car to travel at this speed without sliding A 123 B 0816 C 0736 D 0952 E 0662 Answer B Var 1 57 A car enters a 300m radius horizontal curve on a rainy day when the coefficient of static friction between its tires and the road is 0600 What is the maximum speed at which the car can travel around this curve without sliding A 296 ms B 331 ms C 248 ms D 420 ms E 379 ms Answer D Var 1 58 A car drives over a hilltop that has a radius of curvature 0120 km at the top of the hill At what speed would the car be traveling when it tires just barely lose contact with the road when the car is at the top of the hill A 455 ms B 418 ms C 343 ms D 222 ms E 276 ms Answer C Var 1 59 A 1000kg car is slowly picking up speed as it goes around a horizontal curve whose radius is 100 m The coefficient of static friction between the tires and the road is 0350 At what speed will the car begin to skid sideways A 925 ms B 236 ms C 343 ms D 350 ms E 185 ms Answer E Var 1 60 A 600kg car is going around a banked curve with a radius of l 10 m at a speed of 245 ms What is the appropriate banking angle so that the car stays on its path without the assistance of friction A 2910 B 1350 C 3380 D 5620 E 6090 Answer A Var 5 61 A 600kg car traveling at 245 ms is going around a curve having a radius of 120 m that is banked at an angle of 20 a Is the curve properly banked for the car39s speed b What is the minimum coefficient of static friction required between the road and the car39s tires so the car does not skid Answer a No b 012 Var l 62 A 600kg car traveling at 300 ms is going around a curve having a radius of 120 m that is banked at an angle of 2500 The coefficient of static friction between the car39s tires and the road is 0300 What is the magnitude of the force exerted by friction on the car A 1590 N B 3430 N C 7240 N D 7820 N E 795 N Answer A Var l 63 Engineers are designing a curved section of a highway If the radius of curvature of the curve is 194 m at what angle should the curve be banked so that a car traveling at 290 ms will stay on the road without the aid of frictional forces A 2390 B 1670 C 2100 D 2610 Answer A Var 50 64 The gure shows two wires tied to a 33 kg sphere that revolves in a horizontal circle at constant speed At this particular speed the tension is the SAME in both wires What is the tension f aquot 10 m 60 A 24 N B 32 N C 44 N D 22 N Answer A Var 50 65 The gure shows two wires that are tied to a 710 g mass that revolves in a horizontal circle at a constant speed of 75 ms What is the tension in the upper wire i 2 9 39 10 m 050 m 050 m 10 m A 34 N B 20 N C 27 N D 41 N Answer A Var 50 66 Future space stations will create an arti cial gravity by rotating Consider a cylindrical space station 390 In diameter rotating about its central axis Astronauts walk on the inside surface of the space station What rotation period will provide quotnormalquot gravity A 28 s B 40 s C 63 s D 44 s Answer A Var 50 67 A new roller coaster contains a looptheloop in which the car and rider are completely upside down Ifthe radius of the loop is 132 m with what minimum speed must the car traverse the loop so that the rider does not fall out while upside down at the top Assume the rider is not strapped to the car A 114 ms B 125 ms C 101 ms D 149 ms Answer A Var 50 68 A ball of mass 50 kg is suspended by two wires from a horizontal arm that is attached to a vertical shaft as shown in the figure The shaft is in uniform rotation about its aXis The rate of rotation is adjusted until the tensions in the two wires are EQUAL At that speed the radial acceleration of the ball is closest to 080 m 0 m 060 111 Ball A 49 msz B 59 msz C 69 msz D 79 msZ E 99 msz Answer A Var 1 38 69 A roadway for stunt drivers is designed for racecars moving at a speed of 40 ms A curved section of the roadway is a circular arc of 230 m radius The roadway is banked so that a vehicle can go around the curve with the friction force from the road equal to zero At what angle is the roadway banked A 35 B 37 C 33 D 31 E 29 Answer A Var 50 70 A person on a sled coasts down a hill and then goes over a slight rise with speed 27 ms The top ofthis rise can be modeled as a circle ofradius 41 m The sled and occupant have a combined mass of 110 kg If the coefficient of kinetic friction between the snow and the sled is 010 what friction force is exerted on the sled by the snow as the sled goes over the top of the rise Answer 88 N Var 1 71 A Ferris wheel has diameter of 10 m and makes one revolution in 80 seconds A person weighing 670 N is sitting on one of the benches attached at the rim of the wheel What is the apparent weight that is the normal force exerted on her by the bench of the person as she passes through the highest point of her motion Answer 460 N Var 1 72 The magnitude of the drag force of air resistance on a certain 200kg object is proportional to its speed If the object has a terminal speed 800 ms what is the magnitude of the drag force on the object when it is falling with a speed 300 ms A 196 N B 750 N C 150 N D 735 N E 427 N Answer D Var 1 73 A 300kg object experiences a drag force due to air resistance with a magnitude proportional to the square of its speed The object falls with an acceleration of 400 ms2 downward when it is falling downward at 700 ms What is its terminal speed A 110 ms B 157 ms C 910 ms D 172 ms E 108 ms Answer C Var 1 74 A ship is being pulled through a harbor at constant velocity by two tugboats as shown in the gure The lines attached to the two tugboats have the same tension of 200000 N Each line makes an angle of 2800 with the direction the ship is being towed What is the magnitude of the drag force due to the water on the ship A 177 x 105 N B 188 x 105 N C 939 x 104N D zero E 353 X 105 N Answer E Var 1 75 A 120kg ball is hanging from the end ofa rope The rope hangs at an angle 2500 from the vertical when a 150 ms horizontal wind is blowing If the winds force on the rope is negligible what drag force does the wind exert on the ball A 323 N B 241 N C 368 N D 548 N E 118 N Answer D Var 1 20N39 76 An 80 Urkg object rs faumg and expenehees a drag force due to an39resxstance The v A L L a 1 srhv 4 00 N sZrhzv2 What 15 the termmal speed ofthxs objec rhs 77 r s L 5 22 where vxs the speed ofthe object andb 3 00 N sZrh2 What terminal speedwlll hrs object approach7 A 178 ms 78 The gure shows two forces aehhg on an object wnh magmmdes F178 Nand F2 26 N F A 52 Npomnng down omhng u C 82 Npomtmg down D 82 Npomnng up r An A Var 23 Universig Physics 132 YnllngFreedman Chapter 12 Fluid Mechanics 121 Conceptual Quesuorrs greatest7 D D E The pressure 15 the same at each ofthe labeled porhts Answer E Var 1 treatrhg the Water as mcompressxble 1 re 111 be 1ess th C the abso1ute pressure W111 be greater than 2p Dth gauge pre sure wru hote ange E the gauge pressure W111 rherease but wru not double r E 3 If you double the pressure on the surface of a can of water the buoyant force on a stone placed in that water will A increase but not double B double C decrease but not by onehalf D not change Answer D Var l 4 A cup of water containing an ice cube at 0 C is lled to the brim The tip of the ice cube sticks out of the surface As the ice melts you observe that A the cup over ows B the cup might over ow but it depends on the actual mass of the ice cube C the water level remains the same D the water level actually goes down E There is not enough information to answer this question Answer C Var l 5 Salt water is more dense than fresh water A ship oats in both fresh water and salt water Compared to the fresh water the volume of salt water displaced by the ship is A greater than the volume of fresh water B less than the volume of fresh water C the same as the volume of fresh water Answer B Var l 6 A 50cm3 block of wood is oating partially submerged in water and a 50cm3 block of iron is totally submerged in water Which block has the greater buoyant force on it A the wood B the iron C Both have the same buoyant force D The answer cannot be determined without knowing the densities of the blocks Answer B Var l 7 A rock is under water in a shallow lake As the rock sinks deeper and deeper into water the buoyant force on it A increases B decreases C remains constant Answer C Var l 8 A piece ofwood is oating in a bathtub A second piece of wood sits on top ofthe first piece and does not touch the water If the top piece is taken off and placed in the water what happens to the water level in the tub A It goes up B It goes down C It does not change D This cannot be determined without knowing the volume of the top piece of wood Answer C Var l 9 Water ows through a pipe having a varying width More water ows per second through the wide section than through the narrow section because there is more room for it to ow A True B False Answer B Var l 10 As the speed of a moving uid increases the pressure in the uid A increases B remains constant C decreases D may increase or decrease depending on the density of the uid Answer C Var 1 11 When you blow some air above the upper face of a paper strip the paper rises This occurs because A the air above the upper face of the paper moves faster which makes the pressure higher than at the lower face B the air above the upper face of the paper moves faster which makes the pressure lower than at the lower face C the air above the upper face of the paper moves faster but the pressure remains constant D the air above the upper face of the paper moves slower which makes the pressure higher than at the lower face E the air above the upper face of the paper moves slower which makes the pressure lower than at the lower face Answer B Var l

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