PHYSICS I PHYS 1100
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This 55 page Class Notes was uploaded by Diamond Kirlin MD on Monday October 19, 2015. The Class Notes belongs to PHYS 1100 at Rensselaer Polytechnic Institute taught by Sang-Kee Eah in Fall. Since its upload, it has received 7 views. For similar materials see /class/224880/phys-1100-rensselaer-polytechnic-institute in Physics 2 at Rensselaer Polytechnic Institute.
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Date Created: 10/19/15
H 9quot tb Chapter 1 MEASUREMENT The SI standard of time is based on A the daily rotation of the earth B the frequency of light emitted by Kr86 C the yearly revolution of the earth about the sun D a precision pendulum clock E none of these Ans E A nanosecond is A 109 s B 10 9 s C 10 10 s D 10 10 s E 10 12 Ans B The SI standard of length is based on the distance from the north pole to the equator along a meridian passing through Paris wavelength of light emitted by Hg198 wavelength of light emitted by Kr86 a precision meter stick in Paris the speed of light Ans E Fig0 In 18667 the U S Congress de ned the U S yard as exactly 36003937 international meter This was done primarily because length can be measured more accurately in meters than in yards the meter is more stable than the yard this de nition relates the common U S length units to a more widely used system there are more wavelengths in a yard than in a meter the members of this Congress were exceptionally intelligent Ans C F1150 Which of the following is closest to a yard in length 001 m 01 m 1 m 100 m 1000 m Ans C Fig0 Chapter 1 MEASUREMENT 1 Sm N 9 33 2 There is no SI base unit for area because Fig0 an area has no thickness hence no physical standard can be built we live in a three not a two dimensional world it is impossible to express square feet in terms of meters area can be expressed in terms of square meters area is not an important physical quantity Ans D The SI base unit for mass is Fig0 gram pound kilogram ounce kilopound Ans C A gram is 10 6 kg 10 3 kg 1 kg 103 kg 106 kg Ans B Which of the following weighs about a pound Fig0 005 kg 05 kg 5 kg 50 kg 500 kg Ans D 50 X 104 X 30 X 106 A B C D E 15 X 109 15 X 1010 15 X 1011 15 X 1012 15 X 1013 Ans C 50 X 104 X 30 X 10 6 A B C D E Chapter 1 15 X 10 3 15 X 10 1 15 X 101 15 X 103 15 X 105 Ans B MEASUREMENT 50 X 105 30 X 106 80 X 105 80 X 106 53 X 105 35 X 105 35 X 106 Ans E Fig0 70 X 10620 X 10 6 A 35 X 10 12 B 35 X 10 6 C 35 D 35 X 106 E 35 X 1012 Ans E The number of signi cant gures in 000150 is F1150 manugtoaw Ans B The number of signi cant gures in 150 is 1 00 OTHgtOJM Ans C 03 2 X 27 86 864 8640 Fig0 Chapter 1 MEASUREMENT 3 20 21 22 4 1513 273 29 288 289 2881 28813 Ans B 1 mi is equivalent to 1609 m so 55 mph is A 15 ms B 25 ms C 66 ms D 88 ms E 1500 ms Ans B Fig0 A sphere With a radius of 17 cm has a volume of A 21 X 10 5 n13 B 91 X 10 4 n13 C 36 X 10 3 n13 D 011 n13 E 21 n13 Ans A A sphere With a radius of 17 cm has a surface area of A 21 X 10 5 m2 B 91 X 10 4 m2 C 36 X 10 3 m2 D 011 m2 E 36 m2 Ans C A right circular cylinder With a radius of 23 cm and a height of 14 m has a volume of A 020 n13 B 014 n13 C 93 X 10 3 n13 D 23 X 10 3 n13 E 74 X 10 4 n13 Ans D A right circular cylinder With a radius of 23 cm and a height of 14 cm has a total surface area of A 17 X 10 3 B 32 X 10 3 Ans D Chapter 1 MEASUREMENT 23 24 25 A cubic box With an edge of exactly 1 cm has a volume of A 10 9 n13 B 10 6 n13 C 10 3 n13 D 103 n13 E 106 n13 Ans B A square With an edge of exactly 1 cm has an area of A 10 6 m2 B 10 4 m2 C 102 m2 D 104 m2 E 106 m2 Ans B 1 m is equivalent to 3281 ft A cube With an edge of 15 ft has a volume of A 12 X 102 n13 B 96 X 10 2 n13 C 105 n13 D 95 X 10 2 n13 E 021 n13 Ans B During a short interval of time the speed 1 in ms of an automobile is given by v 1252 72537 Where the time t is in seconds The units of a and b are respectively A m s2 m s4 B s3m s4m C ms2 ms3 D ms3 ms E ms4 ms5 Ans D Suppose A BC7 Where A has the dimension LM and C has the dimension LT Then B has the dimension A TM B LzTM C TML2 D LzTM E MLZT Ans A Chapter 1 MEASUREMENT 5 28 6 Suppose A BTLC 7 Where A has dimensions LT7 B has dimensions LZT 17 and C has dimensions LTZ Then the exponents n and m have the values 23 13 2 3 45 715 15 35 12 12 Ans D Fig0 Chapter 1 MEASUREMENT H 10 9quot th 9 Chapter 2 MOTION ALONG A STRAIGHT LINE A particle moves along the Ir axis from 61 to cf Of the following values of the initial and nal coordinates7 which results in the displacement with the largest magnitude A 51714m7 xf6m B 23174m7 xf78m C 23174m7 xf2m D 51714m7 xf72m E 23174m7 xf4m ans E A particle moves along the 2 axis from cm to 23f Of the following values of the initial and nal coordinates7 which results in a negative displacement A 51714m7 mf6m B 23174m7 xf78m C 23174m7 xf2m D 23174m7 xf72m E 23174m7 xf4m ans B The average speed of a moving object during a given interval of time is always the magnitude of its average velocity over the interval the distance covered during the time interval divided by the time interval one half its speed at the end of the interval its acceleration multiplied by the time interval one half its acceleration multiplied by the time interval Fig0 ans B Two automobiles are 150 kilometers apart and traveling toward each other One automobile is moving at 60 kmh and the other is moving at 40 kmh mph In how many hours will they meet A 25 B 20 C 175 D 15 E 125 ans D A car travels 40 kilometers at an average speed of 80 kmh and then travels 40 kilometers at an average speed of 40kmh The average speed of the car for this 80 km trip is A 40kmh B 45kmh C 48kmh D 53kmh E 80kmh ans D Chapter 2 MOTION ALONG A STRAIGHT LINE 7 Sm N 9 33 F O 8 A car starts from Hither goes 50 km in a straight line to Yon immediately turns around and returns to Hither The time for this round trip is 2 hours The magnitude of the average velocity of the car for this round trip is A 0 B 50 kmhr C 100 kmhr D 200 kmhr E cannot be calculated Without knowing the acceleration ans A A car starts from Hither goes 50 km in a straight line to Yon immediately turns around and returns to Hither The time for this round trip is 2 hours The average speed of the car for this round trip is A 0 B 50 kmh C 100 kmh D 200 kmh E cannot be calculated Without knowing the acceleration ans B The coordinate of a particle in meters is given by x05 1625 7 30253 Where the time t is in seconds The particle is momentarily at rest at t 075 s 13 s 53s 73 s 93s ans B Fig0 A drag racing car starts from rest at t 0 and moves along a straight line With velocity given by v 17252 where b is a constant The expression for the distance traveled by this car from its position at t 0 is bt3 bt33 4bt2 317232 thZ Fig0 ans B A ball rolls up a slope At the end of three seconds its velocity is 20 cms at the end of eight seconds its velocity is 0 What is the average acceleration from the third to the eighth second 25 cms2 40 cms2 50 cms2 60 cms2 667 cms2 ans B Fig0 Chapter 2 MOTION ALONG A STRAIGHT LINE 11 The coordinate of an object is given as a function of time by In 7t 7 32527 Where In is in meters and t is in seconds Its average velocity over the interval from t 0 to t 4s is Fig0 5ms The velocity of an object is given as a function of time by v 4t 7 32527 Where v is in ms and t is in seconds lts average velocity over the interval from t 0 to t 2s Fig0 is 0 is 72 m s is 2 m s is 74 m s cannot be calculated unless the initial position is given ans A The coordinate of an object is given as a function of time by In 4252 7 32537 Where In is in meters and t is in seconds Its average acceleration over the interval from t 0 to t 2s is Fig0 74ms2 4ms2 710ms2 10ms2 713 ms2 ans C Each of four particles move along an In axis Their coordinates in meters as functions of time in seconds are given by Fig0 particle 1 x05 35 7 27253 particle 2 CECE 35 27253 particle 3 x05 35 27252 particle 4 CECE 35 7 34157 27252 Which of these particles have constant acceleration All four Only 1 and 2 Only 2 and 3 Only 3 and 4 None of them ans D Chapter 2 MOTION ALONG A STRAIGHT LINE 9 H F H gt1 10 Each of four particles move along an In axis Their coordinates in meters as functions of time in seconds are given by particle 1 x05 35 7 27253 particle 2 x05 35 27253 particle 3 x05 35 27252 particle 4 x05 35 7 3423 7 27252 Which of these particles is speeding up for t gt 0 A All four B Only 1 C Only 2 and 3 D Only 2 3 and 4 E None of them ans A An object starts from rest at the origin and moves along the CU axis with a constant acceleration of 4ms Its average velocity as it goes from In 2m to CU 8m is A 1ms B 2ms C 3ms D 5ms E 6ms ans E Of the following situations which one is impossible A A body having velocity east and acceleration east B A body having velocity east and acceleration west C A body having zero velocity and non zero acceleration D A body having constant acceleration and variable velocity E A body having constant velocity and variable acceleration ans E Throughout a time interval while the speed of a particle increases as it moves along the c axis its velocity and acceleration might be positive and negative respectively negative and positive respectively negative and negative respectively negative and zero respectively positive and zero respectively F1150 ans C A particle moves on the CU axis When its acceleration is positive and increasing its velocity must be positive its velocity must be negative it must be slowing down it must be speeding up none of the above must be true Fig0 ans E Chapter 2 MOTION ALONG A STRAIGHT LINE 20 2 H 22 2 03 24 The position y of a particle moving along the y axis depends on the time t according to the equation y at 7 17252 The dimensions of the quantities a and b are respectively LZT L3T2 UOWW r H b as none of these ans C A particle moves along the CU axis according to the equation In 62527 where In is in meters and t is in seconds Therefore the acceleration of the particle is 6 ms2 t cannot be negative the particle follows a parabolic path each second the velocity of the particle changes by 98 ms none of the above Fig0 ans E Over a short interval near time t 0 the coordinate of an automobile in meters is given by x05 2725 7 402537 where t is in seconds At the end of 10 s the acceleration of the auto is 27 ms2 40 ms2 740 ms2 712 ms2 724 ms2 Fig0 Over a short interval7 starting at time t 07 the coordinate of an automobile in meters is given by x05 2725 7 402537 where t is in seconds The magnitudes of the initial at t 0 velocity and acceleration of the auto respectively are A 0 12 ms2 B 0 24 ms2 C 27 ms 0 D 27 ms 12 ms2 E 27 ms 24 ms2 ans C At time t 0 a car has a velocity of 16 ms 1t slows down with an acceleration given by 7050257 in ms2 for t in seconds It stops at t A 64 s B 32 s C 16 s D 80 s E 40 s ans D Chapter 2 MOTION ALONG A STRAIGHT LINE 11 25 2 27 2 00 29 12 At time t 0 a car has a velocity of 16 ms 1t slows down with an acceleration given by 705025 in ms2 for t in seconds At the end of 40 s it has traveled 0 12 m 14 m 25 m 59 m ans E A B C D E At time t 0 a car has a velocity of 16 ms It slows down with an acceleration given by 705025 in ms2 for t in seconds By the time it stops it has traveled 15 m 31 m 62 m 85 m 100 m ans D Fig0 Starting at time t 07 an object moves along a straight line with velocity in ms given by t 98 7 22527 where t is in seconds When it momentarily stops its acceleration is C A Starting at time t 07 an object moves along a straight line Its coordinate in meters is given by x05 7525 7 102537 where t is in seconds When it momentarily stops its acceleration is A B C D E A car7 initially at rest7 travels 20 m in 4 s along a straight line with constant acceleration The acceleration of the car is 04 ms2 13 ms2 25 ms2 49 ms2 98 ms2 ans C Fig0 Chapter 2 MOTION ALONG A STRAIGHT LINE 30 3 H 32 3 03 34 A racing car traveling with constant acceleration increases its speed from 10 ms to 50 ms over a distance of 60m How long does this take A 20 s B 40 s C 50 s D 80 s E The time cannot be calculated since the speed is not constant ans B A car starts from rest and goes down a slope with a constant acceleration of 5 ms2 After 5 s the car reaches the bottom of the hill Its speed at the bottom of the hill7 in meters per second7 is 1 125 25 50 160 ans C F1150 A car moving with an initial velocity of 25 ms north has a constant acceleration of 3 ms2 south After 6 seconds its velocity will be 7 ms north 7 ms south 43 ms north 20 ms north 20 ms south ans A Fig0 An object with an initial velocity of 12 ms west experiences a constant acceleration of 4 ms2 west for 3 seconds During this time the object travels a distance of 12 m 24 m 36 m 54 m 144 m ans D Fig0 How far does a car travel in 6 s if its initial velocity is 2 ms and its acceleration is 2 ms2 in the forward direction 12 m 14 m 24 m 36 m 48 m ans E Fig0 Chapter 2 MOTION ALONG A STRAIGHT LINE 13 3 OT 36 37 3 00 39 14 At a stop light7 a truck traveling at 15 ms passes a car as it starts from rest The truck travels at constant velocity and the car accelerates at 3 ms 2 How much time does the car take to catch up to the truck Fig0 5s 10s 15s 20s 25s ans B A ball is in free fall lts acceleration is Fig0 downward during both ascent and descent downward during ascent and upward during descent upward during ascent and downward during descent upward during both ascent and descent downward at all times except at the very top7 when it is zero ans A A ball is in free fall Upward is taken to be the positive direction The displacement of the ball during a short time interval is Fig0 positive during both ascent and descent negative during both ascent and descent negative during ascent and positive during descent positive during ascent and negative during descent none of the above ans D A baseball is thrown vertically into the air The acceleration of the ball at its highest point is Fig0 zero 97 down Which one of the following statements is correct for an object released from rest Fig0 The average velocity during the rst second of time is 49ms During each second the object falls 98m The acceleration changes by 98 ms2 every second The object falls 98m during the rst second of time The acceleration of the object is proportional to its weight ans A Chapter 2 MOTION ALONG A STRAIGHT LINE 4 O 41 4 3 43 44 A freely falling body has a constant acceleration of 98 msz This means that Fig0 the body falls 98 m during each second the body falls 98 m during the rst second only the speed of the body increases by 98 ms during each second the acceleration of the body increases by 98 n1s2 during each second the acceleration of the body decreases by 98 ms2 during each second ans C An object is shot vertically upward While it is rising Fig0 its velocity and acceleration are both upward its velocity is upward and its acceleration is downward its velocity and acceleration are both downward its velocity is downward and its acceleration is upward its velocity and acceleration are both decreasing ans B An object is thrown straight up from ground level with a speed of 50 ms lfg 10 ms2 its distance above ground level 10 s later is Fig0 40m 45m 50m 55m 60m ans B An object is thrown straight up from ground level with a speed of 50 ms lfg 10 ms2 its distance above ground level 60 s later is Fig0 000 m 270 m 330 m 480 m none of these ans E At a location where g 980 n1s27 an object is thrown vertically down with an initial speed of 100 ms After 500 s the object will have traveled Fig0 125 m 1275 m 245 m 250 m 255 m ans B Chapter 2 MOTION ALONG A STRAIGHT LINE 15 45 46 47 48 49 16 An object is thrown vertically upward at 35 ms Taking g 10 ms2 the velocity of the object 5 s later is 70 ms up 15 ms down 15 ms up 85 ms down 85 ms up Fig0 ans B A feather initially at rest is released in a vacuum 12 m above the surface of the earth Which of the following statements is correct The maximum velocity of the feather is 98 ms The acceleration of the feather decreases until terminal velocity is reached The acceleration of the feather remains constant during the fall The acceleration of the feather increases during the fall The acceleration of the feather is zero Fig0 ans C An object is released from rest How far does it fall during the second second of its fall 49 m 98 m 15 m 20 m 25 m ans C Fig0 A heavy ball falls freely starting from rest Between the third and fourth second of time it travels a distance of A 49 m 98 m 294 m 343 m 398 m ans D B C D E As a rocket is accelerating vertically upward at 98 ms2 near Earth s surface it releases a projectile Immediately after release the acceleration in ms2 of the projectile is 98 down 0 98 up 196 up none of the above A B C D E ans A Chapter 2 MOTION ALONG A STRAIGHT LINE 50 5 5 5 5 H 3 3 q A stone is released from a balloon that is descending at a constant speed of 10 ms Neglecting air resistance7 after 20 s the speed of the stone is Fig0 2160 ms 1760 ms 206 ms 196 ms 186 ms ans C An object dropped from the Window ofa tall building hits the ground in 120 S If its acceleration is 980 ms27 the height of the Window above the ground is Fig0 294 m 588 m 118 m 353 m 706 m ans E Neglecting the effect of air resistance a stone dropped off a 175 m high building lands on the ground in Fig0 18s 36s ans C A stone is thrown vertically upward With an initial speed of 195 ms It will rise to a maximum height of A 49 m B 98 m C 194 m D 388 m E none of these ans C A baseball is hit straight up and is caught by the catcher 20 s later The maximum height of the ball during this interval is Fig0 49 m 74 m 98 m 126 m 196 m ans A Chapter 2 MOTION ALONG A STRAIGHT LINE 17 55 56 57 5 00 5 18 An object is thrown straight down with an initial speed of 4 ms from a window which is 8 m above the ground The time it takes the object to reach the ground is 080 s 093 s 13 s 17 s 20 s ans B Fig0 A stone is released from rest from the edge of a building roof 190 m above the ground Ne glecting air resistance7 the speed of the stone7 just before striking the ground7 is A 43 ms B 61 ms C 120 ms D 190 ms E 1400 ms ans B An object is thrown vertically upward with a certain initial velocity in a world where the acceleration due to gravity is 196 ms2 The height to which it rises is that to which the object would rise if thrown upward with the same initial velocity on the Earth Neglect friction A half B M times C twice D four times E cannot be calculated from the given data ans A A projectile is shot vertically upward with a given initial velocity It reaches a maximum height of 100 m If on a second shot7 the initial velocity is doubled then the projectile will reach a maximum height of 707 m 1414 m 200 m 241 m 400 m ans E Fig0 One object is thrown vertically upward with an initial velocity of 100 ms and another object with an initial velocity of 10 ms The maximum height reached by the rst object will be that of the other A 10 times B 100 times C 1000 times D 107 000 times E none of these ans B Chapter 2 MOTION ALONG A STRAIGHT LINE 60 The area under a velocity time graph represents 6 H 62 63 A acceleration B change in acceleration C speed D change in velocity E displacement ans E Displacement can be obtained from A the slope of an acceleration time graph B the slope of a velocity time graph C the area under an acceleration time graph D the area under a velocity time graph E the slope of an acceleration time graph ans D An object has a constant acceleration of 3 ms2 The coordinate versus time graph for this object has a slope that increases With time that is constant that decreases With time of 3 ms of 3 ms2 ans A Fig0 The coordinate time graph of an object is a straight line With a positive slope The object has constant displacement steadily increasing acceleration steadily decreasing acceleration constant velocity steadily increasing velocity Fig0 ans D Chapter 2 MOTION ALONG A STRAIGHT LINE 19 64 Which of the following ve coordinate versus time graphs represents the motion of an object moving With a constant nonzero speed ans B 65 Which of the following ve acceleration versus time graphs is correct for an object moving in a straight line at a constant velocity of 20 ms 1 l l ans E 20 Chapter 2 MOTION ALONG A STRAIGHT LINE 66 Which of the following ve coordinate versus time graphs represents the motion of an object whose speed is increasing ans A 67 A car accelerates from rest on a straight road A short time later7 the car decelerates to a stop and then returns to its original position in a similar manner7 by speeding up and then slowing to a stop Which of the following ve coordinate versus time graphs best describes the motion ans E Chapter 2 MOTION ALONG A STRAIGHT LINE 21 68 The acceleration of an object7 starting from rest7 is shown in the graph below Other than at t 07 when is the velocity of the object equal to zero A During the interval from 10 s to 30 s B At t 35s C At t 40s D At t 50s E At no other time less than or equal to SS ans E 69 An elevator is moving upward with constant acceleration The dashed curve shows the position y of the ceiling of the elevator as a function of the time 25 At the instant indicated by the dot7 a bolt breaks loose and drops from the ceiling Which curve best represents the position of the bolt as a function of time 31 ans B 22 Chapter 2 MOTION ALONG A STRAIGHT LINE 70 The diagram shows a velocity time graph for a car moving in a straight line At point Q the car must be 7 H Fig0 The diagram shows a velocity time graph for moving with zero acceleration traveling downhill traveling below ground level reducing speed traveling in the reverse direction to that at point P ans E a car moving in a straight line At point P the car must be Fig0 moving with zero acceleration climbing the hill accelerating stationary moving at about 45 with respect to the CU axis ans C Chapter 2 MOTION ALONG A STRAIGHT LINE 23 72 73 24 The graph represents the straight line motion of a car How far does the car travel between t2sandt5s vInS 12 i i l l 6 l l l 2 5 9 4m 12m 24m 36m 60m ans D Fig0 The diagram represents the straight line motion of a car Which of the following statements is true vInS 12 i i 2 5 9 The car accelerates7 stops7 and reverses The car accelerates at 6 ms2 for the rst 2 s The car is moving for a total time of 12 s The car decelerates at 12 ms2 for the last 4 s The car returns to its starting point When t 9 s Fig0 ans B Chapter 2 MOTION ALONG A STRAIGHT LINE 74 Consider the following ve graphs note the axes carefully Which of these represents motion at constant speed 0 l IV only IV and V only I7 II7 and III only I and II only I and IV only ans E Fig0 75 An object is dropped from rest Which of the following ve graphs correctly represents its motion The positive direction is taken to be downward U U U ans B Chapter 2 MOTION ALONG A STRAIGHT LINE 25 76 A stone is dropped from a cliff The graph carefully note the axes which best represents its motion while it falls is 0 U ans C 77 An object is thrown vertically into the air Which of the following ve graphs represents the velocity v of the object as a function of the time t The positive direction is taken to be upward ans C 26 Chapter 2 MOTION ALONG A STRAIGHT LINE 1 10 9quot F Chapter 3 VECTORS We say that the displacement of a particle is a vector quantity Our best justi cation for this assertion is A displacement can be speci ed by a magnitude and a direction B operating With displacements according to the rules for manipulating vectors leads to re sults in agreement With experiments a displacement is obviously not a scalar displacement can be speci ed by three numbers displacement is associated With motion Pin ans B The vectors a relationship E and E are related by E 17 Ti Which diagram below illustrates this 7 E None of these ans D A vector of magnitude 3 CANNOT be added to a vector of magnitude 4 so that the magnitude of the resultant is zero 1 3 5 7 ans A Fig0 A vector of magnitude 20 is added to a vector of magnitude 25 The magnitude of this sum might be A zero B C 12 D 47 E 50 ans C Chapter 3 VECTORS 27 9 53 gt1 28 A vector g of magnitude 6 and another vector T have a sum of magnitude 12 The vector T F1150 must have a magnitude of at least 6 but no more than 18 may have a magnitude of 20 cannot have a magnitude greater than 12 must be perpendicular to g must be perpendicular to the vector sum ans A The vector 714T is Fig0 greater than T in magnitude less than A in magnitude in the same direction as l in the direction opposite to A perpendicular to l ans D The vector T73 in the diagram is equal to If Fig0 Fig0 432 ZIHKZ V2V1 l71cos0 Vlcos ans C 14T 3 2 A2 B27 then if and 3 must be parallel and in the same direction l and 3 must be parallel and in opposite directions either l or 3 must be zero the angle between A and 3 must be 60 none of the above is true ans E Chapter 3 VECTORS 9 H H H 3 If lA A B and neither A nor B vanish7 then A 141 and B are parallel and in the same direction B A and B are parallel and in opposite directions C the angle between A and B is 45 D the angle between A and B is 60 E A is perpendicular to B ans A If l D7 A B and neither A nor B vanish7 then A 141 and B are parallel and in the same direction B A and B are parallel and in opposite directions C the angle between A and B is 45 D the angle between A and B is 60 E A is perpendicular to B ans B Four vectors A B7 5 all have the same magnitude The angle 0 between adjacent vectors is 45 as shown The correct vector equation is A 141737 4D0 B 13 Q 7 0 5 0 C4 EQ D Aa Ba C D AO E AC 7B ans B Vectors A and B lie in the my plane We can deduce that A B if A A A B B B AAyBBy C Ax Bx and Ag By D AyAac ByBac E Ax Ag and Bx By ans C Chapter 3 VECTORS 29 30 A vector has a magnitude of 12 When its tail is at the origin it lies between the positive In axis and the negative y axis and makes an angle of 30 With the CU axis Its y component is If Fig0 w 6 6 76 12 ans D the CU component of a vector A in the my plane is half as large as the magnitude of the vector the tangent of the angle between the vector and the CU axis is mp0wgt mwow 12 2 32 3 ans D fl 6 7 8 then 411 has magnitude 10m 20m 30m 40m 50m ans D A vector has a component of 10 m in the HE direction a component of 10m in the 3 direction and a component of 5m in the 2 direction The magnitude of this vector is Fig0 b 3 Fig0 zero 15 m 20 m 25 m 225 m ans B V 200mi 62001117 3001101 The magnitude of i7 is 500m 557m 700m 742m 854m ans C Chapter 3 VECTORS 2 O 2 H 22 A vector in the my plane has a magnitude of 25m and an In component of 12m The angle it makes With the positive In axis is 26 29 61 64 241 ans C Fig0 The angle between T 25 n1 45 and the positive In axis is 29 61 151 209 241 ans B F1150 The angle between T 725 m 45 and the positive In axis is 29 61 119 151 209 ans C Fig0 Let fl 2mi6mji3m l and B 4m i2mj1m The vector sum 3 KB IS A 6mif8mjj2mkA B 72n1A14mAj74mAk C 2mi74mjA4mkA D 8m112mj 73m E none ofthese ans A Let E 2 6mji 3ml and B 4mi 2mj 1m The vector difference D Kigis A 6mif8mji2mkA B 72H1A14H1A 74mk C 2mi74mjA4mkA D mi12mj73m E none of these ans B Chapter 3 VECTORS 31 23 2 q 25 2 32 HA 2mi7 Bm and B 1mi 7 2mj7 then g7 2E A 1 A 13 411 A C 4mii 7m D 4m1 f1mJ A E 74mi 7mj ans A In the diagram7 fl has magnitude 12 m and B has magnitude 8m The In component of fl B is about 55m 76m 12m 14m 15m ans C Fig0 A certain vector in the my plane has an In component of 4m and a y component of 10m It is then rotated in the my plane so its 5v component is doubled Its new y component is about 20 m 72 m 50 m 45 m 22 m ans B A B C D E Vectors fl and 3 each have magnitude LHWhen drawn with their tails at the same point7 the angle between them is 30 The value of A B is A zero B L2 C xng 2 D 2L2 E none of these ans C Chapter 3 VECTORS 27 28 29 30 3 H i6mji 3ml and B 4mi2mj1ml Then Let A 2 m A 8mi 12mj 7 31101 B 12mi7 1411037 201101 C 23 m2 D 17 m2 E none of these ans D Two vectors have magnitudes of 10m and 15m The angle between them when they are drawn with their tails at the same point is 65 The component of the longer vector along the line of the shorter is 0 42 m 63 m 91 m 14 m ans C Fig0 Let g 1 2 2m 1 and T 3 4 m The angle between these two vectors is given by cos 11415 cos 111225 cos 1104225 cos 11115 cannot be found since g and T do not lie in the same plane Fig0 ans D Two vectors lie with their tails at the same point When the angle between them is increased by 20 their scalar product has the same magnitude but changes from positive to negative The original angle between them was A 0 B 60 C 70 D 80 E 90 ans D If the magnitude of the sum of two vectors is less than the magnitude of either vector7 then the scalar product of the vectors must be negative the scalar product of the vectors must be positive the vectors must be parallel and in opposite directions the vectors must be parallel and in the same direction Fig0 none of the above ans A Chapter 3 VECTORS 33 3 3 33 34 35 36 34 If the magnitude of the sum of two vectors is greater than the magnitude of either vector then A the scalar product of the vectors must be negative B the scalar product of the vectors must be positive C the vectors must be parallel and in opposite directions D the vectors must be parallel and in the same direction E none of the above ans E Vectors A and 3 each have magnitude L When drawn with their tails at the same point the angle between them is 60 The magnitude of the vector product A X B is A L22 B L2 c Vin2 D 2L2 E none of these ans C Two vectors lie with their tails at the same point When the angle between them is increased by 20 the magnitude of their vector product doubles The original angle between them was 90 B Two vectors have magnitudes of 10m and 15m The angle between them when they are drawn with their tails at the same point is 65 The component of the longer vector along the line perpendicular to the shorter vector in the plane of the vectors is A 0 42 m 63 m 91 m 14 m ans E B C D E The two vectors 3 7 2 and 2 m 3 7 2m 1 de ne a plane It is the plane of the triangle with both tails at one vertex and each head at one of the other vertices Which of the following vectors is perpendicular to the plane 4mi 6mj 13ml 74mm 6mj 131101 4m 7 6mj 13mm 4mi mi 7 13mm 4 m f 6 m ans A F1100 Chapter 3 VECTORS 37 Let R g X f and 0 y 90 7 where 0 is the angle between g and T when they are drawn with their tails at the same point Which of the following is NOT true 3 3 00 F1150 Rl lgll sin fTXS 650 320 ST0 ansE The value of gtlt is Fig0 zero 1 71 3 3 ans B The value of l gtlt is Fig0 zero 1 71 3 3 ans A Chapter 3 VECTORS 35 03 w H F1150 th 9 36 Chapter 4 MOTION IN TWO AND THREE DIMENSIONS Velocity is de ned as Fig0 rate of change of position with time position divided by time rate of change of acceleration with time a speeding up or slowing down change of position ans A Acceleration is de ned as rate of change of position with time speed divided by time rate of change of velocity with time a speeding up or slowing down change of velocity ans C Which of the following is a scalar quantity Fig0 Speed Velocity Displacement Acceleration None of these ans A Which of the following is a vector quantity Fig0 Mass Density Speed Temperature None of these ans E Which of the following is NOT an example of accelerated motion Fig0 Vertical component of projectile motion Circular motion at constant speed A swinging pendulum Earth s motion about sun Horizontal component of projectile motion ans E Chapter 4 MOTION IN TWO AND THREE DIMENSIONS Sm N 9 33 A particle goes from In 72m y 3m 2 1m to CU 3m y 71m 2 4m Its displacement is 1mi2mi A 5mi74mj f i l l 7lt1mgti7lt2mr 75mi7 2m39 ans B macaw l a E g E l A jet plane in straight horizontal ight passes over your head When it is directly above you the sound seems to come from a point behind the plane in a direction 30 from the vertical The speed of the plane is A the same as the speed of sound B half the speed of sound C three fths the speed of sound D 0866 times the speed of sound E twice the speed of sound ans B A plane traveling north at 200ms turns and then travels south at 200ms The change in its velocity is zero 200 ms north 200 ms south 400 ms north 400 ms south ans E Fig0 Two bodies are falling with negligible air resistance side by side above a horizontal plane If one of the bodies is given an additional horizontal acceleration during its descent it A strikes the plane at the same time as the other body B strikes the plane earlier than the other body C has the vertical component of its velocity altered D has the vertical component of its acceleration altered E follows a straight line path along the resultant acceleration vector ans A The velocity of a projectile equals its initial velocity added to a constant horizontal velocity a constant vertical velocity a constantly increasing horizontal velocity a constantly increasing downward velocity a constant velocity directed at the target Fig0 ans D Chapter 4 MOTION IN TWO AND THREE DIMENSIONS 37 11 A stone thrown from the top of a tall building follows a path that is circular made of two straight line segments hyperbolic parabolic a straight line Fig0 ans D 12 Identical guns re identical bullets horizontally at the same speed from the same height above level planes7 one on the Earth and one on the Moon Which of the following three statements is are true I The horizontal distance traveled by the bullet is greater for the Moon H The ight time is less for the bullet on the Earth III The velocity of the bullets at impact are the same A III only B I and H only C I and HI only D H and HI only E I7 H7 HI ans B 13 A stone is thrown horizontally and follows the path XYZ shown The direction of the acceler ation of the stone at point Y is X I v Y x z39 horizOntal A l B a c i D E ans A 38 Chapter 4 MOTION IN TWO AND THREE DIMENSIONS 14 A bullet shot horizontally from a gun A OW FUD strikes the ground much later than one dropped vertically from the same point at the same instant never strikes the ground strikes the ground at approximately the same time as one dropped vertically from the same point at the same instant travels in a straight line strikes the ground much sooner than one dropped from the same point at the same instant ans C A bomber ying in level ight With constant velocity releases a bomb before it is over the target Neglecting air resistance7 which one of the following is NOT true A B C D E The bomber is over the target When the bomb strikes The acceleration of the bomb is constant The horizontal velocity of the plane equals the vertical velocity of the bomb When it hits the target The bomb travels in a curved path The time of ight of the bomb is independent of the horizontal speed of the plane ans C The airplane shown is in level ight at an altitude of 050 km and a speed of 150 kmh At What distance d should it release a heavy bomb to hit the target X Take 9 10 ms Fig0 2 150 kmh 150 m 295 m 420 m 2550 m 157 000m ans C Chapter 4 MOTION IN TWO AND THREE DIMENSIONS 39 20 40 An object is shot from the back of a railroad atcar moving at 40 kmh on a straight horizontal road The launcher is aimed upward7 perpendicular to the bed of the atcar The object falls in front of the atcar behind the atcar on the atcar either behind or in front of the flatcar7 depending on the initial speed of the object to the side of the atcar ans C Fig0 A ball is thrown horizontally from the top of a 20 m high hill It strikes the ground at an angle of 45 With what speed was it thrown A 14ms B 20ms C 28ms D 32ms E 40ms ans B A stone is thrown outward from the top of a 594 m high cliff with an upward velocity compo nent of 195 ms How long is stone in the air A 400s B 500s C 600s D 700s E 800s ans C A large cannon is red from ground level over level ground at an angle of 30 above the horizontal The muzzle speed is 980 ms Neglecting air resistance7 the projectile will travel what horizontal distance before striking the ground 43 km 85 km 43 km 85 km 170 km ans D F1150 Chapter 4 MOTION IN TWO AND THREE DIMENSIONS 21 A boy on the edge of a vertical cliff 20m high throws a stone horizontally outward with a speed of QOms It strikes the ground at what horizontal distance from the foot of the cliff Use 9 10 ms2 10 m 40 m 50 n1 505n1 none of these Fig0 ans B 22 Which of the curves on the graph below best represents the vertical component vy of the velocity versus the time t for a projectile red at an angle of 45 above the horizontal vy F A B 0 Ct D E A OC B DE C AB D AE E AF ans D Chapter 4 MOTION IN TWO AND THREE DIMENSIONS 41 23 2 q 42 A cannon res a projectile as shown The dashed line shows the trajectory in the absence of gravity points MNOP correspond to the position of the projectile at one second intervals If g 10 n1s27 the lengths X7Y7Z are 5m7 10m7 15m 5m7 20 n17 45m 10m7 40m7 90m 10m7 20m7 30m 02m7 08m7 18m ans B Fig0 A dart is thrown horizontally toward X at QOms as shown It hits Y 01 s later The distance XY is 2m 05m 01 m 005m ans E Fig0 Chapter 4 MOTION IN TWO AND THREE DIMENSIONS 25 26 27 A projectile is red from ground level over level ground with an initial velocity that has a vertical component of 20 ms and a horizontal component of 30 ms Using 9 10ms27 the distance from launching to landing points is 40m 60m 80m 120m 180m ans D Fig0 An object7 tied to a string7 moves in a circle at constant speed on a horizontal surface as shown The direction of the displacement of this object7 as it travels from W to X is A e B l C T D ans E A toy racing car moves with constant speed around the circle shown below When it is at point A its coordinates are In 07 y 3m and its velocity is 6msi When it is at point B its velocity and acceleration are y l A c 76msj and 12ms2i7 respectively 6msi and 712ms2i respectively 6 ms jand 12ms2 i7 respectively F1100 6 ms and 2 ms2 j respectively 6 msj and 07 respectively ans C Chapter 4 MOTION IN TWO AND THREE DIMENSIONS 43 28 29 3 O 31 32 44 An airplane makes a gradual 90 turn While ying at a constant speed of 200 ms The process takes 200 seconds to complete For this turn the magnitude of the average acceleration of the plane is zero 40 ms2 20 ms2 14 ms 10 ms2 ans D 2 Fig0 An airplane is ying north at 500 kmh It makes a gradual 180 turn at constant speed7 changing its direction of travel from north through east to south The process takes 40s The average acceleration of the plane for this turn in kmhs is 125 kmh s7 north 125 kmh s7 east 125 kmh s7 south 25 kmh s7 north 25 kmh s7 south ans E Fig0 An object is moving on a circular path of radius 7T meters at a constant speed of 40ms The time required for one revolution is 2712 s 7722 s 7T2 s 7724 271 s ans B UQW A particle moves at constant speed in a circular path The instantaneous velocity and instan taneous acceleration vectors are both tangent to the circular path both perpendicular to the circular path perpendicular to each other opposite to each other none of the above Fig0 ans C A stone is tied to a string and Whirled at constant speed in a horizontal circle The speed is then doubled Without changing the length of the string Afterward the magnitude of the acceleration of the stone is the same twice as great four times as great half as great one fourth as great Fig0 ans C Chapter 4 MOTION IN TWO AND THREE DIMENSIONS 33 34 35 36 37 Two objects are traveling around di erent circular orbits With constant speed They both have the same acceleration but object A is traveling twice as fast as object B The orbit radius for object A is the orbit radius for object B A one fourth B one half C the same as D twice E four times ans E A stone is tied to a 050 m string and Whirled at a constant speed of 40ms in a vertical circle Its acceleration at the top of the circle is A 98 ms27 up B 98 ms27 down C 80ms27 down D 32ms27 up E 32ms27 down ans E A stone is tied to a 050 m string and Whirled at a constant speed of 40ms in a vertical circle Its acceleration at the bottom of the circle is A 98 ms27 up B 98 ms27 down C 80 ms27 up D 32ms27 up E 32ms27 down ans D A car rounds a 20 m radius curve at 10 ms The magnitude of its acceleration is A0 B 020ms2 C 50ms2 D 40ms2 E 400ms2 ans C For a biological sample in a 10 m radius centrifuge to have a centripetal acceleration of 259 its speed must be A 11ms B 16ms C 50ms D 122ms E 245ms ans B Chapter 4 MOTION IN TWO AND THREE DIMENSIONS 45 38 A girl jogs around a horizontal circle with a constant speed She travels one fourth of a 39 40 4 46 H revolution a distance of 25m along the circumference of the circle in 50 s The magnitude of her acceleration is A 031ms2 B 13ms2 C 16ms2 D 39ms2 E 63ms2 ans C A stone is tied to the end of a string and is swung with constant speed around a horizontal circle with a radius of 15m If it makes two complete revolutions each second the magnitude of its acceleration is A 024ms2 B 24ms2 C 24ms2 D 240ms2 E 2400ms2 ans D A Ferris wheel with a radius of 80m makes 1 revolution every 10s When a passenger is at the top essentially a diameter above the ground he releases a ball How far from the point on the ground directly under the release point does the ball land 0 10 m 80 m 91 m 16 m ans D Fig0 A boat is able to move through still water at 20ms It makes a round trip to a town 30 km upstream If the river ows at 5ms the time required for this round trip is 120 s 150 s 200 s 300 s 320 s ans E Fig0 Chapter 4 MOTION IN TWO AND THREE DIMENSIONS 42 4 03 44 A boat is traveling upstream at 14 kmh with respect to a river that is owing at 6kmh with respect to the ground A man runs directly across the boat7 from one side to the other7 at 6kmh with respect to the boat The speed of the man with respect to the ground is 10 kmh 14 kmh 185 kmh 21 kmh 26 kmh ans A Fig0 A ferry boat is sailing at 12kmh 30 W of N with respect to a river that is owing at 60kmh As observed from the shore7 the ferry boat is sailing 30 E of N due N 30 W of N 45 E of N none of these muowaw ans B A boy wishes to row across a river in the shortest possible time He can row at 2ms in still water and the river is owing at 1 ms At what angle 0 should he point the bow front of his boat 30 45 60 63 90 Fig0 Chapter 4 MOTION IN TWO AND THREE DIMENSIONS 47 45 A girl wishes to swim across a river to a point directly opposite as shown She can swim at 2ms in still water and the river is owing at 1 ms At what angle 0 with respect to the line joining the starting and nishing points should she swim 30 45 60 63 90 ans A Fig0 46 A motor boat can travel at 10 kmh in still water A river ows at 5 kmh west A boater wishes to cross from the south bank to a point directly opposite on the north bank At what angle must the boat be headed A 27 E of N B 30 E of N C 45 E of N D 60 E of N E depends on the width of the river ans B 47 Two projectiles are in ight at the same time The acceleration of one relative to the other is always 98 ms2 can be as large as 198 ms2 is zero A B C can be horizontal D E none of these ans D 48 Chapter 4 MOTION IN TWO AND THREE DIMENSIONS H 10 9quot th 9 Chapter 5 FORCE AND MOTION I An example of an inertial reference frame is any reference frame that is not accelerating a frame attached to a particle on which there are no forces any reference frame that is at rest a reference frame attached to the center of the universe a reference frame attached to Earth Fig0 ans B An object moving at constant velocity in an inertial frame must A have a net force on it B eventually stop due to gravity C not have any force of gravity on it D have zero net force on it E have no frictional force on it ans D 1n SI units a force is numerically equal to the 7 When the force is applied to it A velocity of the standard kilogram B speed of the standard kilogram C velocity of any object D acceleration of the standard kilogram E acceleration of any object ans D Which of the following quantities is NOT a vector Mass Displacement Weight Acceleration Force Fig0 ans A A newton is the force of gravity on a 1kg body of gravity on a 1g body that gives a 1 g body an acceleration of 1 cms2 that gives a 1kg body an acceleration of 1 ms2 Fig0 that gives a 1kg body an acceleration of 98 ms2 ans D Chapter 5 FORCE AND MOTION 7 I 49 Sm N 9 33 50 The unit of force called the newton is A 98 kg m s2 B 1 kg m s2 C de ned by means of Newton s third law D 1 kg of mass E 1 kg of force ans B A force of 1 N is 1kgs 1kg ms 1kg 1kg m2s 1kg m2s2 ans C ms2 Fig0 The standard 1 kg mass is attached to a compressed spring and the spring is released If the mass initially has an acceleration of 56 ms 7 the force of the spring has a magnitude of A 28 N B 56 N C 112 N D 0 E an undetermined amount ans B Acceleration is always in the direction A of the displacement B of the initial velocity C of the nal velocity D of the net force E opposite to the frictional force ans D The term mass refers to the same physical concept as A weight B inertia C force D acceleration C volume ans B Chapter 5 FORCE AND MOTION 7 I 11 The inertia of a body tends to cause the body to H b Fig0 speed up slow down resist any change in its motion fall toward Earth decelerate due to friction ans C A heavy ball is suspended as shown A quick jerk on the lower string will break that string but a slow pull on the lower string will break the upper string The rst result occurs because Fig0 v5 lower string the force is too small to move the ball action and reaction is operating the ball has inertia air friction holds the ball back the ball has too much energy ans C When a certain force is applied to the standard kilogram its acceleration is 50 ms2 When the same force is applied to another object its acceleration is one fth as much The mass of the object is Fig0 02 kg 05 kg 10 kg 50 kg 10kg ans D Mass differs from weight in that Fig0 all objects have weight but some lack mass weight is a force and mass is not the mass of an object is always more than its weight mass can be expressed only in the metric system there is no difference ans B Chapter 5 FORCE AND MOTION 7 I 51 52 The mass of a body Fig0 is slightly different at different places on Earth is a vector is independent of the free fall acceleration is the same for all bodies of the same volume can be measured most accurately on a spring scale ans C The mass and weight of a body Fig0 differ by a factor of 98 are identical are the same physical quantities expressed in different units are both a direct measure of the inertia of the body have the same ratio as that of any other body placed at that location ans E An object placed on an equal arm balance requires 12 kg to balance it When placed on a spring scale the scale reads 12 kg Everything balance scale set of weights and object is now transported to the Moon where the free fall acceleration is one sixth that on Earth The new readings of the balance and spring scale respectively are Fig0 12 kg 72 kg ans C Two objects one having three times the mass of the other are dropped from the same height in a vacuum At the end of their fall their velocities are equal because Fig0 anything falling in vacuum has constant velocity all objects reach the same terminal velocity the acceleration of the larger object is three times greater than that of the smaller object the force of gravity is the same for both objects none of the above ans E A feather and a lead ball are dropped from rest in vacuum on the Moon The acceleration of the feather is Fig0 more than that of the lead ball the same as that of the lead ball less than that of the lead ball 98 m s2 zero since it oats in a vacuum ans B Chapter 5 FORCE AND MOTION 7 I 2 O 2 H 22 The block shown moves with constant velocity on a horizontal surface Two of the forces on it are shown A frictional force exerted by the surface is the only other horizontal force on the block The frictional force is 0 2 N leftward 2 N rightward slightly more than 2N leftward slightly less than 2N leftward ans B Fig0 Two forces one with a magnitude of 3N and the other with a magnitude of 5N are applied to an object For which orientations of the forces shown in the diagrams is the magnitude of the acceleration of the object the least ans A A crate rests on a horizontal surface and a woman pulls on it with a 10 N force Rank the situations shown below according to the magnitude of the normal force exerted by the surface on the crate least to greatest 10N 10N 177 quot x 39 x x 39 39 x 39 39 quot 39 x 39 x 39 1 2 3 A 1 2 3 B 2 1 3 C 2 3 1 D 1 3 2 E 3 2 1 ans E Chapter 5 FORCE AND MOTION 7 I 53 23 2 q 25 26 54 A heavy wooden block is dragged by a force E along a rough steel plate7 as shown in the diagrams for two cases The magnitude of the applied force F is the same for both cases The normal force in ii7 as compared With the normal force in is less for some angles of the incline and greater for others a less or greater7 depending on the magnitude of the applied force F Fig0 T ans C Equal forces E act on isolated bodies A and B The mass of B is three times that of A The magnitude of the acceleration of A is A three times that of B B 13 that of B C the same as B D nine times that of B E 19 that of B ans A A car travels east at constant velocity The net force on the car is A east B west C up D down E zero ans E A constant force of 80 N is exerted for 40 s on a 16 kg object initially at rest The change in speed of this object Will be A 05ms B 2ms C 4ms D 8ms E 32ms ans B Chapter 5 FORCE AND MOTION 7 I
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