Deck 5: Kinetic Energy, work, and Power

Question 1

A force has the dependence F_x = -ax⁴ on the position x,with the constant a = 25.0 N/m⁴.The work performed by this force when the position of its point of application changes from 0.75 m to 1.25 m is

A)- 17.4 J.
B)17.4 J.
C)- 14.1 J.
D)14.1 J.
E)0 J.

Answer 1

- 14.1 J.

Question 2

Initially an object of mass 1.00 kg is moving to the left at 10.0 m/s.If 150 J of work is done on the object,then how fast will it be moving?

A)17.3 m/sec
B)20.0 m/sec
C)25.0 m/sec
D)27.3 m/sec

Answer 2

20.0 m/sec

Question 3

The kinetic energy of a 1.2-kg toy train is 3.6 J.What is its speed?

A)1.7 m/s
B)6.0 m/s
C)2.0 m/s
D)2.4 m/s
E)3.0 m/s

Answer 3

2.4 m/s

Question 4

A 1.2-kg toy train is moving with a speed of 2.0 m/s.What is its kinetic energy?

A)1.0 J
B)1.2 J
C)1.8 J
D)2.2 J
E)2.4 J

Question 5

A 5.0-kg crate is lifted straight up from the ground at a constant speed of 1.5 m/s to the back of a moving truck which is at a height of 5.0 m above the ground.What power is needed to accomplish this task?

A)25 W
B)53 W
C)74 W
D)87 W
E)101 W

Question 6

Two cars are moving.The first car has twice the mass of the second car,but only half as much kinetic energy.Then,both cars increase their speed by 8.00 m/s.They then have the same kinetic energy.The original speeds of the two cars are,respectively,

A)v₁ = 5.66 m/s,v₂ = 11.3 m/s.
B)v₁ = 14.1 m/s,v₂ = 7.07 m/s.
C)v₁ = 11.3 m/s,v₂ = 5.66 m/s.
D)v₁ = 22.6 m/s,v₂ = 11.3 m/s.
E)v₁ = 14.1 m/s,v₂ = 22.6 m/s.

Question 7

A lift is used to raise objects to the back of a moving truck.If the maximum power the lift is capable of delivering is 98 W,what is the maximum constant speed with which this lift can raise a 5.0 kg crate straight up from the ground to the back of the moving truck? The back of the moving truck is 5.0 m above the ground.

A)19 m/s
B)2.0 m/s
C)1.5 m/s
D)7.0 m/s
E)3.2 m/s

Question 8

A 1000-kg car starts from rest and accelerates to 60 mph (27 m/s)in 6.0 s.How much horsepower is required for this to occur?

A)52 hp
B)63 hp
C)75 hp
D)81 hp
E)95 hp

Question 9

A 20.0-kg object starts from rest and slides down an inclined plane.The change in its elevation is 2.50 m and its final speed is 5.00 m/sec.How much energy did the object lose due to friction as it slid down the plane?

A)241 J
B)245 J
C)250 J
D)491 J

Question 10

You pull sled with a rope which makes an angle of 30 ^$\circ$ to the horizontal and the tension in the rope is 40.0 N.Calculate the work you do on the sled if it moves 100 m.

A)1.22 kJ.
B)2.00 kJ.
C)3.46 kJ.
D)4.57 kJ.
E)5.00 kJ.

Question 11

A force has the dependence F_x = -ax⁴ on the position x.The work performed by this force when the position of its point of application changes from 0.75 m to 1.50 m is -32.2 J.the constant a is

A)23.2 N/m⁴
B)19.1 N/m⁴
C)25.0 N/m⁴
D)29.3 N/m⁴
E)21.9 N/m⁴

Question 12

An electron's initial position is zero and its final position is 1.00 m.The electric force on the electron is to the left and its magnitude is ,where F is measured in newtons and x is measured in meters.How much work does the electric force do on the electron as it moves?

A)- 0.865 J
B)- 0.432 J
C)0.432 J
D)0.865 J

Question 13

If the kinetic energy of a sub-atomic particle was doubled,then by what factor would its speed increase?

A)the square root of two
B)two
C)four
D)eight

Question 14

A spring of negligible mass is compressed by 0.250 m.Then a steel ball bearing of mass 0.05 kg is put on the spring,and the spring is released.The spring and ball bearing are aligned horizontally and friction is negligible.In addition,assume that the ball bearing will come off the spring exactly as the spring returns to its equilibrium position.The speed of the ball bearing right after the ball bearing loses contact with the spring is 12.9 m/s.What is the spring constant of the spring?

A)200 N/m
B)123 N/m
C)112 N/m
D)133 N/m
E)51.0 N/m

Question 15

A 3.0-kg crate rests at the bottom of a plane inclined at an angle of 15.0 ^$\circ$ above the horizontal.The crate is given a push up the plane and when it has travelled a distance of 2.0 m up the plane its speed is 3.0 m/s.How much work is done on the crate by gravity?

A)-15 J
B)-60 J
C)-30 J
D)-45 J
E)-10 J

Question 16

If the speed of a sub-atomic particle was tripled,then by what factor would its kinetic energy increase?

A)nine
B)three
C)the square root of three
D)twenty seven

Question 17

A car of mass 1250 kg,can reach the 60 mph (=26.8 m/s)mark in 5.25 seconds.What is the average power needed to accomplish this?

A)91.3 kW
B)85.5 kW
C)78.4 kW
D)65.2 kW
E)43.8 kW

Question 18

A force of 40.0 N is applied to a crate to displace it by 50.0 m.How much work is done on the crate by this force?

A)1.25  10³ J
B)1.50  10³ J
C)2.00  10³ J
D)2.25  10³ J

Question 19

A spring of negligible mass and with spring constant 200.0 N/m is compressed by 0.250 m.Then a steel ball bearing of mass 0.05 kg is put on the spring,and the spring is released.The spring and ball bearing are aligned horizontally and friction is negligible.In addition,assume that the ball bearing will come off the spring exactly as the spring returns to its equilibrium position.The speed of the ball bearing right after the ball bearing loses contact with the spring is

A)12.9 m/s.
B)14.2 m/s.
C)15.8 m/s.
D)11.3 m/s.
E)17.6 m/s.

Question 20

What is the average power output of an engine when a car of mass m accelerates from rest to a final speed v over a distance d on flat,level ground? Ignore energy lost due to friction and air resistance.

A)mv²/d
B)mv²/2d
C)mv³/2d
D)mv³/4d

Question 21

A 30.0 kg ball is released from rest and is acted upon by a net force of -1.40  10¹⁶ r ^-2 (the force pulls the ball towards r = 0).The ball starts from rest at an initial position of r_i = 6.39  10⁶ m and moves under the influence of the force to a final position of r_f= 6.38  10⁶.What is the kinetic energy of the ball when it reaches its final position,r_f?

A)2.94  10⁶ J.
B)9.22  10⁶ J.
C)1.58  10⁶ J.
D)3.75  10⁶ J.
E)3.43  10⁶ J.

Question 22

A 15,000-kg train accelerates uniformly from 0 to 15 m/s when passing through a distance of 150 m.What is its kinetic energy when it is 75 m down the track?

A)420 kJ
B)600 kJ
C)840 kJ
D)1200 kJ
E)1700 kJ

Question 23

A 30.0 kg ball is released from rest and is acted upon by a net force of -1.40  10¹⁶ r ^-2 (the force pulls the ball towards r = 0).The ball starts from rest at an initial position of r_i = 6.39  10⁶ m and moves under the influence of the force to a final position of r_f= 6.38  10⁶.What is the speed of the ball when it reaches its final position,r_f?

A)552 m/s
B)531 m/s
C)478 m/s
D)442 m/s
E)404 m/s

Question 24

Two boats are travelling along a river.Boat A is half as massive as boat B,but is going 3 times as fast.What is the ratio of kinetic energies K_A/K_B?

A)0.11
B)0.22
C)1.5
D)4.5
E)9

Question 25

Two boats are travelling along a river.Boat A is half as massive as boat B,but the kinetic energy of boat A is 3 larger than the kinetic energy of boat B.What is the ratio of their speeds v_A/v_B?

A)6.0
B)1.2
C)1.5
D)0.82
E) 2.4

Question 26

A mass attached to a horizontal spring,and resting on a frictionless surface is free to oscillate back and forth.Suppose the spring is stretched a distance 2d from equilibrium,and released.As the mass passes through the origin,how does its speed compare to the same mass and spring if stretched initially only a distance d from equilibrium?

A)two times greater
B)two times smaller
C)square root of 2 times greater
D)square root of 2 times smaller

Question 27

A student raises a 1-kg textbook 1 m off the surface of a table.How does the work done by gravity W_g on the book compare to the work done by the student W_s on the book?

A)W_g > W_s
B)W_g < W_s
C)W_g = W_s
D)None are correct.
E)More information is needed.

Question 28

A variable force of the form F=3x² + 2x + 5 N acts on a 2 kg object as it moves from x = 2 m to x = 3 m.How much work is done by this force?

A)-29 J
B)29 J
C)-18 J
D)18 J
E)17 J

Question 29

An ideal spring requires 50 J to be compressed by 15 cm.The value of the spring constant of this spring is

A)2222 N/m.
B)667 N/m.
C)4444 N/m.
D)5648 N/m.
E)1245 N/m.

Question 30

The Concorde was the fastest passenger airliner to ever fly,with an operating mass of 78,700 kg and a maximum cruising kinetic energy of 1.38  10¹⁰ J.What is the maximum cruising speed of the Concorde?

A)1825 km/hr
B)1845 km/hr
C)2200 km/hr
D)2132 km/hr
E)2195 km/hr

Question 31

When a 2 kg object is at x = 2 m it has a velocity 2.5 m/s in the positive x-direction.The object is subjected to a single force of the form F=3x² + 2x + 5 N as it moves from x = 2 m to x = 4 m.what is the speed of the object when its location is x = 4 m?

A)5.5 m/s
B)10.m/s
C)8.8 m/s
D)9.2 m/s
E)7.5 m/s

Question 32

A 65-kg skydiver moving at terminal speed falls 40 m in 1 second.The power the skydiver is expending on the air is

A)34 hp.
B)26 hp.
C)9.8 hp.
D)3.5 hp.

Question 33

A woman of mass 50 kg runs up a flight of stairs.If each step is 20 cm high and her power is 180 W,how many stairs can she climb in 30 seconds?

A)60
B)55
C)42
D)38

Question 34

What is the force that a baseball pitcher must apply to a 145 g baseball over a distance of 2.2 m to give it a speed of 144 km/hr when the ball is released? Assume that the force is constant.

A)25.8 N
B)52.7 N
C)109 N
D)115 N
E)127 N

Question 35

The force acting on a 30.0 kg ball is -1.20  10¹⁶ r ^-2 (the force pulls the ball towards r = 0).An externally applied force moves the ball slowly from an initial distance of r_i = 6.38  10⁶ m to a final position of r_f= 6.39  10⁶.The work done by the applied force is

A)2.94  10⁶ J.
B)9.22  10⁶ J.
C)1.58  10⁶ J.
D)3.75  10⁶ J.
E)922 J.

Question 36

A spring,with k = 2500N/m,is fixed vertically to the floor.A 10.0-kg box is pressed down on the spring such that the total compression of the spring is 0.5 m.Assuming the work done against drag (air resistance)is 60 J,how high will the box reach above its release position?

A)1.23 m
B)2.01 m
C)2.58 m
D)0.5 m
E)1.57 m

Question 37

How much work is done on a 7.26-kg shot by the shot putter if he launches shot at 45.0 ^$\circ$ ,and it lands 23.0 m from the launch point (ignore the height of the shot putter).

A)396 J
B)579 J
C)792 J
D)819 J

Question 38

A man of mass 60 kg runs up a flight of 60 steps in 40 seconds.If each step is 20 cm high,his power is

A)240 W.
B)177 W.
C)134 W.
D)18 W.

Question 39

An engine with 75 kW of power can accelerate a car from rest to 20 m/s during 6.0 s.What is the mass of the car (ignore friction and air resistance)?

A)1.25  10³ kg
B)2.25  10³ kg
C)3.25  10³ kg
D)2.65  10³ kg
E)1.85  10³ kg

Question 40

A construction worker with a mass of 89 kg is able to jump from a height of 1.5 m and land safely by squatting down at a uniform rate as he lands.He squats down over a distance of 0.69 m.The force (in N)exerted by his legs during the squatting process is

A)133.
B)1309.
C)1898.
D)2312.

Question 41

A horizontal spring having constant k = 50.0 N/m is attached to a block having mass 0.50 kg.The mass is oscillating freely on a frictionless table with amplitude 15.0 cm.As the mass travels from the position of maximum stretch to half the position of maximum stretch,how much work is done by the spring on the mass?

A)+0.28 J
B)-0.42 J
C)-0.28 J
D)+0.14 J
E)+0.42 J

Question 42

A ball of mass 1.5 kg is shot horizontally from a building of height of 11 m with a velocity of 10 m/s.What is the kinetic energy of the ball when it hits the ground?

A)23.2 J
B)9800 J
C)15.0 J
D)911 J
E)237 J

Question 43

What power delivered by a motor is required to raise a 5.00 kg object 10.0 m vertically at a constant speed in 3.30 seconds? (1 hp = 746 W)

A)0.25 hp
B)0.20 hp
C)0.22 hp
D)0.29 hp
E)2.2 hp

Question 44

An object slides without friction down an incline and loses height h = 131 m.The incline makes an angle of 35.0 ^$\circ$ with respect to the horizontal.If the object started with a speed of 45.0 m/s,what will be its final speed in m/s?

A)57.2
B)45.0
C)21.1
D)67.8
E)90.0

Question 45

A motor developing 0.250 hp raises a 5.00 kg object 10.0 m vertically at a constant speed.How long does it take to accomplish this task? (1 hp = 746 W)

A)0.541 s
B)1.23 s
C)2.63 s
D)4.56 s
E)7.21 s

Question 46

A baby (m=7.1 kg)lies in his bed,1.1 m above the ground.The father (m = 81 kg)then lifts him up to 1.9 m above the ground and then places him on the ground.How much total work does the father do in moving his child?

A)-800 J
B)-76 J
C)-56J
D)+56J

Question 47

The Statue of Freedom stands above the US Capital Dome.She is made of bronze,has a mass of 6800 kg,and stands 6.0 m tall and the top of her head is 88 m above the ground.How much work was done in lifting her up to the top of the Capital Dome (assume she was in the standing position when they started lifting her)?

A)5.6  10⁵ J
B)5.5  10⁶ J
C)5.9  10⁶ J
D)6.3  10⁵ J

Question 48

An object slides without friction down an incline and loses a height h = 51.0 m.The incline makes an angle of 35.0 ^$\circ$ with respect to the horizontal.If the object's final speed was 45.0 m/s,what was its initial speed in m/s?

A)45.0
B)34.7
C)38.1
D)28.1
E)32.0

Question 49

An object slides without friction up an incline and gains a height h = 71.0 m.The incline makes an angle of 35.0 ^$\circ$ with respect to the horizontal.If the object started with a speed of 45.0 m/s,what will be its final speed in m/s?

A)45.0
B)29.7
C)25.1
D)58.5
E)35.0

Question 50

In the figure,a force F is being applied to the block with a magnitude such that it moves up along the frictionless inclined place with a constant velocity of 5 m/s.The angle in the figure is 30 ^$\circ$ ,and the mass of the block is 50 kg.How much work (in Joules)is done by the force F in moving the block 10 meters along the surface of the inclined plane (within 5% accuracy)?

A)500 J
B)2500 J
C)4200 J
D)5000 J
E)zero

Question 51

A constant force of 41.5 N,directed at 32.9 from horizontal,pulls a mass of 12.7 kg horizontally a distance of 3.33 m.Calculate the work done by the force.(in J).

A)8.04  10¹
B)9.09  10¹
C)1.03  10²
D)1.16  10²
E)1.31  10²

Question 52

A rope that makes an angle of 28 degrees with respect to the vertical is used to pull a sled.The sled has a mass of 35 kg and the tension in the rope is 17 N.How much work is done by the force of the rope if the sled moves a horizontal distance of 5.6 m?

A)1900 J
B)200 J
C)45 J
D)84 J
E)95 J

Question 53

A ball of mass 5.00 kg is thrown from the ground at an angle of 20.0 ^$\circ$ from the vertical with a speed of 20.0 m/s.The ball lands on top of a building that is 10.0 m tall.What is the speed of the ball in m/s just before it lands on the roof of the building?

A)8.95
B)10.0
C)12.5
D)14.3
E)16.9

Question 54

A horizontal spring having constant k = 50.0 N/m is attached to a block having mass 0.50 kg.The mass is oscillating freely on a frictionless table with amplitude 15.0 cm.As the mass travels from equilibrium to half the position of maximum stretch,how much work is done by the spring on the mass?

A)+0.14 J
B)-0.14 J
C)+0.28 J
D)-0.28 J

Question 55

An object slides without friction up an incline and gains a height h = 71.0 m.The incline makes an angle of 35.0 ^$\circ$ with respect to the horizontal.If the object's final speed was 45.0 m/s,what was its initial speed in m/s?

A)56.3
B)53.1
C)45.0
D)70.0
E)58.5

Question 56

A spring with spring constant k is suspended from the ceiling.When a mass of M kg is attached to the spring,it stretches d₁ m.The mass is then pulled down an additional d₂ m and let go.Which one of the following statements about the resulting motion is true?

A)The maximum kinetic energy is (1/2)kd₁.
B)The maximum kinetic energy is (1/2)kd₁².
C)The maximum kinetic energy is (1/2)kd₂.
D)The maximum kinetic energy is (1/2)kd₂².
E)The maximum kinetic energy is -kd₂.

Question 57

A rope that makes an angle of 28 degrees with respect to the horizontal is used to pull a sled.The sled has a mass of 35 kg and the tension in the rope is 17 N.How much work is done by the force of the rope if the sled moves a horizontal distance of 5.6 m?

A)45 J
B)84 J
C)95 J
D)200 J
E)1900 J

Question 58

A crane with an efficiency of 0.8 takes 20 s to lift a load of 50 kg to a height of 200 m.How much power does it take to run the crane (within 5% accuracy)?

A)4.9·10³ W
B)6.1·10³ W
C)1.0·10⁵ W
D)1.2·10⁵ W
E)2.4·10⁶ W

Question 59

A car with a mass of 1000 kg is traveling at 20 m/s.How fast does a person on a bicycle with a total mass of 100 kg have to travel such that they have the same kinetic energy as the car?

A)20 m/s
B)63 m/s
C)126 m/s
D)200 m/s
E)2000 m/s

Question 60

How much work does a weight-lifter do in holding a 245-kg weight 2.13 m over the ground?

A)0 J
B)522 J
C)3400 J
D)5110 J

Question 61

A 60% efficient engine is used to haul 200 kg steel beams up to the ninth floor.How much energy needs to be supplied to the engine to lift the beams from the second floor 20 m below?

A)200 J
B)65,400 J
C)3920 J
D)14,540 J
E)6880 J

Question 62

A mass of 0.75 kg is suspended from a spring.If 1.41 J of work is done against the spring as the mass is pulled 0.15 m away from its equilibrium position,what is the spring constant of the spring?

A)76.3 N/m
B)49.1 N/m
C)125 N/m
D)98.1 N/m
E)25.0 N/m

Question 63

A spring has a spring constant of 25 N/m,and a mass of 0.75 kg is suspended from it.If the mass is pulled down 0.13 m away from its equilibrium position,what is the work done against the spring?

A)0 J
B)0.21 J
C)0.75 J
D)5.88 J
E)1.41 J

Question 64

A 10.0-g bullet traveling horizontally with an initial speed of v strikes a fixed wooden block.The bullet comes to rest 22 cm inside the block.The magnitude of the force exerted on the bullet by the block over its 22-cm travel is shown in graph.The maximum value of the force is F_max = 1.47  10³ N.What is the initial speed of the bullet?

A)280 m/s
B)400 m/s
C)220 m/s
D)100 m/s
E)200 m/s

Question 65

Calculate the kinetic energy of a baby of mass 4.6 kg,riding in a car at a speed of 53.3 miles/hour.

A)9.24 J
B)31.4 J
C)421 J
D)1300 J
E)72,300 J

Question 66

A 0.5-kg ball is thrown vertically upward with an initial velocity of 10 m/s.What is the change in the ball's kinetic energy between the starting point and the highest point in the trajectory?

A)-25 J
B)-5 J
C)0 J
D)5 J
E)25 J

Question 67

An ideal spring is attached to the ceiling.Without anything attached to the bottom of the spring,the bottom of the spring is 40 cm below the ceiling.When a 3.0 kg mass is attached to the bottom of the spring,the bottom of the spring (at rest)is 65 cm below the ceiling.What is the spring constant of the spring?

A)29 N/m
B)45 N/m
C)74 N/m
D)120 N/m
E)940 N/m

Question 68

A car of mass 1000 kg is accelerated from a velocity of 10 m/s to 30 m/s in a time of 5 s.What is the work done during the acceleration (within 5% accuracy;ignore frictional forces)?

A)zero
B)4·10⁴ J
C)8·10⁴ J
D)4·10⁵ J
E)8·10⁵ J

Question 69

A spring attached to the ceiling is stretched 100 mm when a mass of 2 kg is hung on its end.How much work must be done to compress the spring by 6 cm?

A)0 J
B)0.35 J
C)7.1 J
D)390 J
E)5.9 kJ

Question 70

A 10.0-g bullet traveling at 200 m/s strikes a fixed wooden block.The bullet comes to rest 22 cm inside the block.The magnitude of the force exerted on the bullet by the block over its 22-cm travel is shown in graph.Find the value of F_max.

A)1.21  10³ N
B)1.21  10⁵ N
C)1.46  10³ N
D)1.46  10⁵ N
E)2.13  10⁴ N