Deck 6: Work and Energy

Question 1

A force with a magnitude of 25 N and directed at an angle of 37° above the horizontal is used to move a 10-kg crate along a horizontal surface at constant velocity.How much work is done by this force in moving the crate a distance of 15 m?

A)zero joules
B)1.7 J
C)40 J
D)98 J
E)300 J

Answer 1

300 J

Question 2

A concrete block is pulled 7.0 m across a frictionless surface by means of a rope.The tension in the rope is 40 N; and the net work done on the block is 247 J.What angle does the rope make with the horizontal?

A)28°
B)41°
C)47°
D)62°
E)88°

Answer 2

28°

Question 3

The kinetic energy of a car is 8 × 10⁶ J as it travels along a horizontal road.How much work is required to stop the car in 10 s?

A)zero joules
B)8 × 10⁴ J
C)8 × 10⁵ J
D)8 × 10⁶ J
E)8 × 10⁷ J

Answer 3

8 × 10⁶ J

Question 4

A 1.0-kg ball on the end of a string is whirled at a constant speed of 2.0 m/s in a horizontal circle of radius 1.5 m.What is the work done by the centripetal force during one revolution?

A)zero joules
B)2.7 J
C)6.0 J
D)25 J
E)33 J

Question 5

A stationary 4-kg shell explodes into three pieces.Two of the fragments have a mass of 1 kg each and move along the paths shown with a speed of 10 m/s.The third fragment moves upward as shown.
In which one of the following situations is zero net work done?

A)A ball rolls down an inclined plane.
B)A physics student stretches a spring.
C)A projectile falls toward the surface of Earth.
D)A box is pulled across a rough floor at constant velocity.
E)A child pulls a toy across a rough surface causing it to accelerate.

Question 6

Which one of the following has the largest kinetic energy?

A)a raindrop falling
B)a woman swimming
C)a jet airplane flying at its maximum speed
D)the earth moving in its orbit around the sun
E)the space shuttle orbiting the Earth

Question 7

A constant force of 25 N is applied as shown to a block which undergoes a displacement of 7.5 m to the right along a frictionless surface while the force acts.What is the work done by the force?

A)zero joules
B)+94 J
C)-94 J
D)+160 J
E)-160 J

Question 8

A car is traveling at 7.0 m/s when the driver applies the brakes.The car moves 1.5 m before it comes to a complete stop.If the car had been moving at 14 m/s, how far would it have continued to move after the brakes were applied? Assume the braking force in both cases is constant and the same.

A)1.5 m
B)3.0 m
C)4.5 m
D)6.0 m
E)7.5 m

Question 9

Which one of the following situations is an example of an object with a non-zero kinetic energy?

A)a drum of diesel fuel on a parked truck
B)a stationary pendulum
C)a satellite in geosynchronous orbit
D)a car parked at the top of a hill
E)a boulder resting at the bottom of a cliff

Question 10

Which one of the following statements concerning kinetic energy is true?

A)Kinetic energy can be measured in watts.
B)Kinetic energy is always equal to the potential energy.
C)Kinetic energy is always positive.
D)Kinetic energy is a quantitative measure of inertia.
E)Kinetic energy is directly proportional to velocity.

Question 11

In which one of the following situations will there be an increase in kinetic energy?

A)A projectile approaches its maximum height.
B)A ball starts from rest and freely rolls downhill.
C)A box is pulled across a rough floor at constant speed.
D)A satellite travels in a circular orbit around the earth at fixed altitude.
E)A stone at the end of a string is whirled in a horizontal circle at constant speed.

Question 12

Complete the following statement: Work may be expressed using all of the following units except

A)N . m.
B)joule.
C)erg.
D)ft . lb.
E)watt.

Question 13

A 5.00-kg block of ice is sliding across a frozen pond at 2.00 m/s.A 7.60-N force is applied in the direction of motion.After the ice block slides 15.0 m, the force is removed.The work done by the applied force is

A)-114 J.
B)+114 J.
C)-735 J.
D)+735 J.
E)+19.7 J.

Question 14

How much energy is dissipated in braking a 1200-kg car to a stop from an initial speed of 30 m/s?

A)24 000 J
B)280 000 J
C)540 000 J
D)820 000 J
E)12 000 J

Question 15

Mike is cutting the grass using a human-powered lawn mower.He pushes the mower with a force of 45 N directed at an angle of 41° below the horizontal direction.Calculate the work that Mike does on the mower each time he pushes it 9.1 m across the yard.

A)510 J
B)260 J
C)410 J
D)360 J
E)310 J

Question 16

An experimental 1500-kg car travels at a constant speed of 22 m/s around a circular test track that is 80 m across.What is the kinetic energy of the car?

A)zero joules
B)3.6 × 10⁵ J
C)3.3 × 10⁴ J
D)1.6 × 10⁴ J
E)7.2 × 10⁵ J

Question 17

Use the work-energy theorem to find the force required to accelerate an electron (m = 9.11 × 10^-31 kg) moving along the x axis from 4.00 × 10⁶ m/s to 1.60 × 10⁷ m/s in a distance of 0.0125 m.

A)8.75 × 10^-15 N
B)5.47 × 10^-22 N
C)8.20 × 10^-17 N
D)1.64 × 10^-14 N
E)3.56 × 10^-19 N

Question 18

The kinetic energy of an 1800-kg truck is 7.2 × 10⁵ J.What is the speed of the truck?

A)25 m/s
B)33 m/s
C)28 m/s
D)17 m/s
E)21 m/s

Question 19

Julie carries an 8.0-kg suitcase as she walks 18 m along a horizontal walkway to her hotel room at a constant speed of 1.5 m/s.How much work does Julie do in carrying her suitcase?

A)zero joules
B)40 J
C)200 J
D)300 J
E)2000 J

Question 20

A 10.0-g bullet traveling horizontally at 755 m/s strikes a stationary target and stops after penetrating 14.5 cm into the target.What is the average force of the target on the bullet?

A)1.97 × 10⁴ N
B)2.07 × 10⁵ N
C)6.26 × 10³ N
D)3.13 × 10⁴ N
E)3.93 × 10⁴ N

Question 21

Which one of the following choices is an example of a conservative force?

A)tension
B)normal force
C)static frictional force
D)motor propulsion force
E)elastic spring force

Question 22

A 2.0-kg projectile is fired with initial velocity components v_ox = 30 m/s and v_oy = 40 m/s from a point on the earth's surface.Neglect any effects due to air resistance.
How much work was done in firing the projectile?

A)900 J
B)1600 J
C)2500 J
D)4900 J
E)9800 J

Question 23

Two balls of equal size are dropped from the same height from the roof of a building.One ball has twice the mass of the other.When the balls reach the ground, how do the kinetic energies of the two balls compare?

A)The lighter one has one fourth as much kinetic energy as the other does.
B)The lighter one has one half as much kinetic energy as the other does.
C)The lighter one has the same kinetic energy as the other does.
D)The lighter one has twice as much kinetic energy as the other does.
E)The lighter one has four times as much kinetic energy as the other does.

Question 24

A rock is thrown straight up from the surface of the Earth.Which one of the following statements describes the energy transformation of the rock as it rises? Neglect air resistance.

A)The total energy of the rock increases.
B)The kinetic energy increases and the potential energy decreases.
C)Both the potential energy and the total energy of the rock increase.
D)The kinetic energy decreases and the potential energy increases.
E)Both the kinetic energy and the potential energy of the rock remain the same.

Question 25

An elevator supported by a single cable descends a shaft at a constant speed.The only forces acting on the elevator are the tension in the cable and the gravitational force.Which one of the following statements is true?

A)The magnitude of the work done by the tension force is larger than that done by the gravitational force.
B)The magnitude of the work done by the gravitational force is larger than that done by the tension force.
C)The work done by the tension force is zero joules.
D)The work done by the gravitational force is zero joules.
E)The net work done by the two forces is zero joules.

Question 26

A donkey pulls a crate up a rough, inclined plane at constant speed.Which one of the following statements concerning this situation is false?

A)The gravitational potential energy of the crate is increasing.
B)The net work done by all the forces acting on the crate is zero joules.
C)The work done on the crate by the normal force of the plane is zero joules.
D)The donkey does "positive" work in pulling the crate up the incline.
E)The work done on the object by gravity is zero joules.

Question 27

A pebble rolls off the roof of Science Hall and falls vertically.Just before it reaches the ground, the pebble's speed is 17 m/s.Neglect air resistance and determine the height of Science Hall.

A)42 m
B)33 m
C)26 m
D)21 m
E)15 m

Question 28

A block is dropped from a high tower and is falling freely under the influence of gravity.Which one of the following statements is true concerning this situation? Neglect air resistance.

A)As the block falls, the net work done by all of the forces acting on the block is zero joules.
B)The kinetic energy increases by equal amounts over equal distances.
C)The kinetic energy of the block increases by equal amounts in equal times.
D)The potential energy of the block decreases by equal amounts in equal times.
E)The total energy of the block increases by equal amounts over equal distances.

Question 29

A woman stands on the edge of a cliff and throws a stone vertically downward with an initial speed of 10 m/s.The instant before the stone hits the ground below, it has 450 J of kinetic energy.If she were to throw the stone horizontally outward from the cliff with the same initial speed of 10 m/s, how much kinetic energy would it have just before it hits the ground?

A)50 J
B)100 J
C)450 J
D)800 J
E)950 J

Question 30

Which one of the following choices is an example of a non-conservative force?

A)gravitational force
B)electrical force
C)kinetic frictional force
D)elastic spring force

Question 31

A roller-coaster car is moving at 20 m/s along a straight horizontal track.What will its speed be after climbing the 15-m hill shown in the figure, if friction is ignored?

A)17 m/s
B)7 m/s
C)5 m/s
D)10 m/s
E)14 m/s

Question 32

A 12-kg crate is pushed up an incline from point A to point B as shown in the figure.What is the change in the gravitational potential energy of the crate?

A)+590 J
B)-590 J
C)+1200 J
D)-1200 J
E)This cannot be determined without knowing the angle of the incline.

Question 33

During the construction of a high rise building, 40-kg block is vertically lifted 20 meters from the surface of the earth.To one significant figure, what is the change in the gravitational potential energy of the block?

A)+800 J
B)-800 J
C)+8000 J
D)-8000 J
E)zero joules

Question 34

In which one of the following systems is there a decrease in gravitational potential energy?

A)a boy stretches a horizontal spring
B)a girl jumps down from a bed
C)a crate rests at the bottom of an inclined plane
D)a car ascends a steep hill
E)water is forced upward through a pipe

Question 35

Complete the following statement: A force that acts on an object is said to be conservative if

A)it obeys Newton's laws of motion.
B)it results in a change in the object's kinetic energy.
C)it always acts in the direction of motion of the object.
D)the work it does on the object is independent of the path of the motion.
E)the work it does on the object is equal to the increase in the object's kinetic energy.

Question 36

A 2.0-kg projectile is fired with initial velocity components v_ox = 30 m/s and v_oy = 40 m/s from a point on the earth's surface.Neglect any effects due to air resistance.
What is the kinetic energy of the projectile when it reaches the highest point in its trajectory?

A)zero joules
B)900 J
C)1600 J
D)2500 J
E)4900 J

Question 37

Larry's gravitational potential energy is 1870 J as he sits 2.20 m above the ground in a sky diving airplane before it takes off.What is Larry's gravitational potential energy when be begins to jump from the airplane at an altitude of 923 m?

A)7.85 × 10⁵ J
B)1.87 × 10³ J
C)3.29 × 10⁴ J
D)9.36 × 10² J
E)4.22 × 10⁶ J

Question 38

Two boxes are connected to each other as shown.The system is released from rest and the 1.00-kg box falls through a distance of 1.00 m.The surface of the table is frictionless.What is the kinetic energy of box B just before it reaches the floor?

A)2.45 J
B)4.90 J
C)9.80 J
D)29.4 J
E)39.2 J

Question 39

A 1500-kg elevator moves upward with constant speed through a vertical distance of 25 m.How much work was done by the tension in the elevator cable?

A)990 J
B)8100 J
C)140 000 J
D)370 000 J
E)430 000 J

Question 40

A helicopter (m = 3250 kg) is cruising at a speed of 56.9 m/s at an altitude of 185 m.What is the total mechanical energy of the helicopter?

A)3.91 × 10⁷ J
B)5.26 × 10⁷ J
C)2.27 × 10⁸ J
D)6.91 × 10⁷ J
E)1.12 × 10⁸ J

Question 41

How much power is needed to lift a 75-kg student vertically upward at a constant speed of 0.33 m/s?

A)12.5 W
B)25 W
C)115 W
D)230 W
E)243 W

Question 42

An escalator is 30.0 meters long and slants at 30.0° relative to the horizontal.If it moves at 1.00 m/s, at what rate does it do work in lifting a 50.0-kg woman from the bottom to the top of the escalator?

A)49.3 W
B)98.0 W
C)245 W
D)292 W
E)495 W

Question 43

A 9.0-kg box of oranges slides from rest down a frictionless incline from a height of 5.0 m.A constant frictional force, introduced at point A, brings the block to rest at point B, 19 m to the right of point A.

-What is the coefficient of kinetic friction, $\mu$ _k, of the surface from A to B?

A)0.11
B)0.26
C)0.33
D)0.47
E)0.52

Question 44

A dam is used to block the passage of a river and to generate electricity.Approximately 5.73 *10⁴ kg of water fall each second through a height of 19.6 m.If 85 % of the gravitational potential energy of the water were converted to electrical energy, how much power would be generated?

A)9.36 *10⁶ W
B)1.52 *10⁷ W
C)1.08 *10⁷ W
D)1.35 * 10⁸ W
E)4.68 * 10⁶ W

Question 45

What power is needed to lift a 49-kg person a vertical distance of 5.0 m in 20.0 s?

A)12.5 W
B)25 W
C)60 W
D)120 W
E)210 W

Question 46

A block of mass m is released from rest at a height R above a horizontal surface.The acceleration due to gravity is g.The block slides along the inside of a frictionless circular hoop of radius R.
What is the magnitude of the normal force exerted on the block by the hoop when the block reaches the bottom of the hoop?

A)zero newtons
B)mg²/R
C)mg
D)2mg
E)3mg

Question 47

A roller coaster starts from rest at the top of an 18-m hill as shown.The car travels to the bottom of the hill and continues up the next hill that is 10.0 m high. How fast is the car moving at the top of the 10.0-m hill, if friction is ignored?

A)6.4 m/s
B)8.1 m/s
C)13 m/s
D)18 m/s
E)27 m/s

Question 48

A block of mass m is released from rest at a height R above a horizontal surface.The acceleration due to gravity is g.The block slides along the inside of a frictionless circular hoop of radius R.
Which one of the following expressions gives the speed of the mass at the bottom of the hoop?

A)zero m/s²
B)v = mgR
C)
D)
E)v² = 2gR

Question 49

A skier leaves the top of a slope with an initial speed of 5.0 m/s.Her speed at the bottom of the slope is 13 m/s.What is the height of the slope?

A)1.1 m
B)4.6 m
C)6.4 m
D)7.3 m
E)11 m

Question 50

The kinetic energy of a car is 8 × 10⁶ J as it travels along a horizontal road.How much power is required to stop the car in 10 s?

A)zero watts
B)8 × 10⁴ W
C)8 × 10⁵ W
D)8 × 10⁶ W
E)8 × 10⁷ W

Question 51

A block of mass m is released from rest at a height R above a horizontal surface.The acceleration due to gravity is g.The block slides along the inside of a frictionless circular hoop of radius R.
A physics student shoves a 0.50-kg block from the bottom of a frictionless 30.0° inclined plane.The student performs 4.0 J of work and the block slides a distance s along the incline before it stops.Determine the value of s.

A)8.0 cm
B)16 cm
C)82 cm
D)160 cm
E)330 cm

Question 52

A bicyclist is traveling at a speed of 20.0 m/s as he approaches the bottom of a hill.He decides to coast up the hill and stops upon reaching the top.Neglecting friction, determine the vertical height of the hill.

A)28.5 m
B)3.70 m
C)11.2 m
D)40.8 m
E)20.4 m

Question 53

A 9.0-kg box of oranges slides from rest down a frictionless incline from a height of 5.0 m.A constant frictional force, introduced at point A, brings the block to rest at point B, 19 m to the right of point A.
What is the speed of the box just before it reaches point A?

A)98 m/s
B)21 m/s
C)9.9 m/s
D)5.7 m/s
E)4.4 m/s

Question 54

An engineer is asked to design a playground slide such that the speed a child reaches at the bottom does not exceed 6.0 m/s. Determine the maximum height that the slide can be.

A)1.8 m
B)2.9 m
C)3.2 m
D)4.5 m
E)7.4 m

Question 55

A 3.0-kg cylinder falls vertically from rest in a very tall, evacuated tube near the surface of the earth.What is its speed after the cylinder has fallen 6.0 m?

A)8.0 m/s
B)11 m/s
C)13 m/s
D)120 m/s
E)26 m/s

Question 56

A 51-kg woman runs up a flight of stairs in 5.0 s.Her net upward displacement is 5.0 m.Approximately, what average power did the woman exert while she was running?

A)5.0 kW
B)1.0 kW
C)0.75 kW
D)0.50 kW
E)0.25 kW

Question 57

An automobile approaches a barrier at a speed of 20 m/s along a level road.The driver locks the brakes at a distance of 50 m from the barrier.What minimum coefficient of kinetic friction is required to stop the automobile before it hits the barrier?

A)0.4
B)0.5
C)0.6
D)0.7
E)0.8

Question 58

A care package is dropped from rest from a helicopter hovering 25 m above the ground.What is the speed of the package just before it reaches the ground? Neglect air resistance.

A)22 m/s
B)16 m/s
C)12 m/s
D)8.0 m/s
E)5.0 m/s

Question 59

The initial velocity of a 4.0-kg box is 11 m/s, due west.After the box slides 4.0 m horizontally, its speed is 1.5 m/s.Determine the magnitude and the direction of the non-conservative force acting on the box as it slides.

A)42 N, due west
B)120 N, due east
C)31 N, due east
D)59 N, due east
E)83 N, due west

Question 60

A warehouse worker uses a forklift to raise a crate of pickles on a platform to a height 2.75 m above the floor.The combined mass of the platform and the crate is 207 kg.If the power expended by the forklift is 1440 W, how long does it take to lift the crate?

A)37.2 s
B)5.81 s
C)3.87 s
D)18.6 s
E)1.86 s

Question 61

The force component acting on an object along the displacement varies with the displacement s as shown in the graph.Determine the work done on the object as it travels from s = 0.0 to 12 m.

A)48 J
B)66 J
C)72 J
D)57 J
E)81 J

Question 62

What minimum coefficient of kinetic friction is required to bring the crate to a stop over a distance of 5.0 m along the lower surface?

A)0.30
B)0.32
C)0.60
D)0.66
E)0.76

Question 63

A 325-N force accelerates a 50.0-kg crate from rest along a horizontal frictionless surface for a distance of 20.0 m as shown in the figure.
What is the final speed of the crate?

A)11.4 m/s
B)16.1 m/s
C)32.2 m/s
D)131 m/s
E)259 m/s

Question 64

The amount of energy needed to power a 0.10-kW bulb for one minute would be just sufficient to lift a 1.0-kg object through a vertical distance of

A)12 m
B)75 m
C)100 m
D)120 m
E)610 m

Question 65

A top fuel dragster with a mass of 500.0 kg starts from rest and completes a quarter mile (402 m) race in a time of 5.0 s.The dragster's final speed is 130 m/s.Neglecting friction, what average power was needed to produce this final speed?

A)140 hp
B)750 hp
C)1100 hp
D)2.7 × 10⁴ hp
E)8.5 × 10⁵ hp

Question 66

A 0.50-kg ball on the end of a rope is moving in a vertical circle of radius 3.0 m near the surface of the Earth where the acceleration due to gravity, g, is 9.8 m/s².Point A is at the top of the circle; C is at the bottom.Points B and D are exactly halfway between A and C.
Which one of the following statements concerning the tension in the rope is true?

A)The tension is smallest at A.
B)The tension is smallest at C.
C)The tension is smallest at both B and D.
D)The tension is the same at A and C.
E)The tension is the same at A, B, C, and D.

Question 67

A 325-N force accelerates a 50.0-kg crate from rest along a horizontal frictionless surface for a distance of 20.0 m as shown in the figure.
How much work is done on the crate?

A)1.62 × 10² J
B)7.70 × 10² J
C)3.82 × 10³ J
D)6.50 × 10³ J
E)1.50 × 10⁴ J

Question 68

A 12.5-kg crate slides along a horizontal frictionless surface at a constant speed of 4.0 m/s.The crate then slides down a frictionless incline and across a second horizontal surface as shown in the figure.
What is the kinetic energy of the crate as it slides on the upper surface?

A)30 J
B)80 J
C)100 J
D)200 J
E)490 J

Question 69

A motorist driving a 1000-kg car wishes to increase her speed from 20 m/s to 30 m/s in 5 s.Determine the horsepower required to accomplish this increase.Neglect friction.

A)20 hp
B)30 hp
C)70 hp
D)80 hp
E)90 hp

Question 70

A rope exerts a force on a 20.0-kg crate.The crate starts from rest and accelerates upward at 5.00 m/s² near the surface of the earth.
What is the kinetic energy of the crate when it is 4.0 m above the floor?

A)400 J
B)250 J
C)116 J
D)704 J
E)1180 J

Question 71

A 325-N force accelerates a 50.0-kg crate from rest along a horizontal frictionless surface for a distance of 20.0 m as shown in the figure.
What coefficient of friction would be required to keep the crate moving at constant speed under the action of the 325-N force?

A)0.250
B)0.321
C)0.508
D)0.663
E)0.747

Question 72

A 0.50-kg ball on the end of a rope is moving in a vertical circle of radius 3.0 m near the surface of the Earth where the acceleration due to gravity, g, is 9.8 m/s².Point A is at the top of the circle; C is at the bottom.Points B and D are exactly halfway between A and C.
The ball moves on the circle from A to C under the influence of gravity alone.If the kinetic energy of the ball is 35 J at A, what is its kinetic energy at C?

A)zero joules
B)29 J
C)35 J
D)44 J
E)64 J

Question 73

What is the speed of the crate when it arrives at the lower surface?

A)7.7 m/s
B)8.6 m/s
C)59 m/s
D)75 m/s
E)98 m/s

Question 74

The graph shows the force component along the displacement as a function of the magnitude of the displacement.Determine the work done by the force during the interval from 2 to 10 m.

A)140 J
B)190 J
C)270 J
D)450 J
E)560 J

Question 75

What is the kinetic energy of the crate as it slides on the lower surface?

A)290 J
B)320 J
C)370 J
D)470 J
E)570 J

Question 76

A rope exerts a force on a 20.0-kg crate.The crate starts from rest and accelerates upward at 5.00 m/s² near the surface of the earth.
How much work was done by the force in raising the crate 4.0 m above the floor?

A)399 J
B)250 J
C)116 J
D)704 J
E)1180 J

Question 77

Which one of the following is not a unit of energy?

A)foot . pound
B)kilowatt .hour
C)newton . meter
D)watt
E)joule

Question 78

While the crate slides along the upper surface, how much gravitational potential energy does it have compared to what it would have on the lower surface?

A)80 J
B)100 J
C)240 J
D)370 J
E)490 J