Deck 6: Work and Energy

Question 1

The weight of an object on the moon is one-sixth its weight on Earth. A body moving with a given speed on the moon has kinetic energy equal to ______________ it would have if it were moving at the same speed on Earth.

A) the kinetic energy
B) 1/36 the kinetic energy
C) 1/6 the kinetic energy
D) 6 times the kinetic energy
E) 36 times the kinetic energy

Answer 1

the kinetic energy

Question 2

Use the figure to answer the next question. A light rope runs through two frictionless pulleys of negligible mass. A mass, m, is hung from one of the pulleys and a force, F is applied to one end of the rope so that the mass moves at a constant speed.
A car and its occupants, with a total mass m, are moving at a speed v relative to an observer on the side of the road. You are driving in another car, also traveling at speed v, and in the same direction as the first car. The kinetic energy of the first car relative to you is

A) 0
B) mv²
C) m(2v)²
D) m (3v)²
E) depends on the mass of your car

Answer 2

0

Question 3

A 5-kg object slides down a frictionless surface inclined at an angle of 30º from the horizontal. The total distance moved by the object along the plane is 10 meters. The work done on the object by the normal force of the surface is

A) zero
B) 0.50 kJ
C) 0.43 kJ
D) 0.58 kJ
E) 0.25 kJ

Answer 3

zero

Question 4

Initially a body moves in one direction and has kinetic energy K. Then it moves in the opposite direction with three times its initial speed. What is the kinetic energy now?

A) K
B) 3K
C) -3K
D) 9K
E) -9K

Question 5

A particle moves halfway around a circle of radius R. It is acted on by a radial force of magnitude F. The work done by the radial force is

A) zero
B) FR
C) F $\pi$ R
D) 2FR
E) 2 $\pi$ R

Question 6

Negative work means

A) the kinetic energy of the object increases.
B) the applied force is variable.
C) the applied force is perpendicular to the displacement.
D) the applied force is opposite to the displacement.
E) nothing; there is no such thing as negative work.

Question 7

Use the figure to answer the next question. A light rope runs through two frictionless pulleys of negligible mass. A mass, m, is hung from one of the pulleys and a force, F is applied to one end of the rope so that the mass moves at a constant speed.
If the force is applied over a distance, d, the distance the mass moves is

A) 0
B) d
C) d
D) d
E) 2d

Question 8

Two parents moving into a new house attempt to pull a large crate down a large hallway. One parent applies a force of magnitude 150 N directed 45 degrees to the direction of motion, while the other parent applies a force of 120 N on the other side of the direction of motion. If they move the crate 15 m and perform work at 2.6 kJ, at what angle to the direction of motion did the second parent pull on the crate?

A) 54 degrees
B) 30 degrees
C) 60 degrees
D) 34 degrees
E) 56 degrees

Question 9

A force pushes a block along a horizontal surface against a force of friction _f. If the block undergoes a displacement s at constant velocity, the work done by the resultant force on the block

A) is equal to the work done by the force of friction _f
B) is given by W = ·
C) increases the kinetic energy of the block.
D) increases the potential energy of the block.
E) is zero.

Question 10

The kinetic energy of a car is 1.00 $\times$ 10⁵ J. If the car's speed is increased by
20 percent, the kinetic energy of the car becomes

A) 4.00 $\times$ 10³ J
B) 1.20 $\times$ 10⁵ J
C) 1.44 $\times$ 10⁵ J
D) 1.04 $\times$ 10⁵ J
E) unknown; the answer depends on the mass of the car, which is not given

Question 11

A body moves with decreasing speed. Which of the following statements is true?

A) The net work done on the body is positive, and the kinetic energy is increasing.
B) The net work done on the body is positive, and the kinetic energy is decreasing.
C) The net work done on the body is zero, and the kinetic energy is decreasing.
D) The net work done on the body is negative, and the kinetic energy is increasing.
E) The net work done on the body is negative, and the kinetic energy is decreasing.

Question 12

If mechanical work is done on a body, the body must

A) accelerate.
B) be in equilibrium.
C) not exert any force.
D) have no friction force exerted on it.
E) move.

Question 13

Use the figure to answer the next question. A light rope runs through two frictionless pulleys of negligible mass. A mass, m, is hung from one of the pulleys and a force, F is applied to one end of the rope so that the mass moves at a constant speed.
What is the force needed to move the mass at a constant speed?

A) 0
B) mg
C) mg
D) 2mg
E) 4mg

Question 14

A bullet with a mass of 12 g moving horizontally strikes a fixed block of wood and penetrates a distance of 5.2 cm. The speed of the bullet just before the collision is 640 m/s. The average force that the wood exerted on the bullet was

A) 4.7 $\times$ 10⁴ N
B) 74 N
C) 4.7 $\times$ 10⁶ N
D) unknown; the mass of the wood is required
E) None of these is correct.

Question 15

Two forces, both of magnitude 12 N and directed 35 degrees either side of the direction of motion, pull a crate 15 m. How much work is done by the forces in moving the crate?

A) 1.8 $\times$ 10² J
B) 1.5 $\times$ 10² J
C) 2.9 $\times$ 10² J
D) 2.9 $\times$ 10² N/m
E) 2.1 $\times$ 10² J

Question 16

A constant force of 45 N directed at angle $\theta$ to the horizontal pulls a crate of weight 100 N from one end of a room to another a distance of 4 m. Given that the vertical component of the pulling force is 12 N, calculate the work done by the force in moving the crate.

A) 4.1 $\times$ 10² J
B) 48.0 J
C) 3.9 $\times$ 10² N/m
D) 1.7 $\times$ 10² J
E) 3.9 $\times$ 10³ J

Question 17

The average marathon runner can complete the 42.2-km distance of the marathon in 3 h and 30 min. If the runner's mass is 75 kg, what is the runner's average kinetic energy during the run?

A) 842 J
B) 5.45 $\times$ 10³ J
C) 251 J
D) 126 J
E) 421 J

Question 18

The work expended to accelerate a car from 0 to 30 m/s

A) is more than that required to accelerate it from 30 m/s to 60 m/s.
B) is equal to that required to accelerate it from 30 m/s to 60 m/s.
C) is less than that required to accelerate it from 30 m/s to 60 m/s.
D) can be any of the preceding, depending on the time taken.
E) is described by none of these statements.

Question 19

The SI unit of energy can be expressed as

A) kg · m/s
B) kg · m/s²
C) m/(kg · s)
D) kg · m · s²
E) None of these is correct.

Question 20

The work-kinetic energy theorem states that

A) work done on an object is converted into kinetic energy and vice versa.
B) work done on an object comes from the kinetic energy.
C) work and kinetic energy are the same thing.
D) work and kinetic energy cannot co-exists at the same time.
E) none of the above.

Question 21

Use the figure to answer the question. The graph shows the speed of a light truck of mass 4000 kg coasting on neutral down a level straight road. The truck is slowing down due to air resistance and rolling friction.
Estimate the work done per second by the retarding force at t = 5s.

A) 20 kJ
B) 40 kJ
C) 60 kJ
D) 80 kJ
E) 100 kJ

Question 22

The angle between the vector = + 2 + 3k and the x axis is approximately

A) 17º
B) 26º
C) 37º
D) 58º
E) 75º

Question 23

What is the work done by a car's braking system when it slows the 1500-kg car from an initial speed of 96 km/h down to 56 km/h in a distance of 55 m?

A) 8.3 kJ
B) 20 kJ
C) 1.3 MJ
D) 2.5 MJ
E) 8.3 MJ

Question 24

Car drag racing takes place over a distance of a mile (402 m) from a standing start. If a car (mass 1500 kg) could be propelled forward with a pulling force equal to that of gravity, what would be the change in kinetic energy and the terminal speed of the car (in mph) at the end of the race be? (For comparison, a modern, high-performance sports car may reach a terminal speed of just over 100 mph = 44.7 m/s.)

A) 604 kJ and 28.4 m/s
B) 5.92 kJ and 88.9 m/s
C) 5.92 MJ and 7900 m/s
D) 3680 kJ and 70.0 m/s
E) 5.92 MJ and 88.9 m/s

Question 25

A mass m = 2.5 kg is sliding along a frictionless table with initial speed v as shown in the figure. It strikes a coiled spring that has a force constant k = 500 N/m and compresses it a distance x₂ - x₁ = -5.0 cm. The initial speed v of the block was

A) 0.71 m/s
B) 1.0 m/s
C) 1.4 m/s
D) 0.50 m/s
E) 1.7 m/s

Question 26

A variable force is represented on an F-versus-x graph. Which of the following is the work done by this force?

A) the slope of the curve
B) the area bounded by the curve and the x axis
C) the area bounded by the curve and the F axis
D) the F value multiplied by the x value
E) the F value divided by the x value

Question 27

In a television tube, an electron starting from rest experiences a force of 4.0 $\times$ 10^-15 N over a distance of 50 cm. The final speed of the electron is (do not worry about relativistic effects):

A) 4.4 $\times$ 10¹⁵ m/s
B) 6.6 $\times$ 10⁷ m/s
C) 3.3 $\times$ 10⁷ m/s
D) 1.3 $\times$ 10⁸ m/s
E) 6.6 $\times$ 10⁸ m/s

Question 28

A particle that is subjected to a variable force travels a distance of 20 m in a straight line in the same direction as the force. The force varies as follows:
First, 5.0 m and F = 0
Next, 5.0 m and F = 3.0 N
Next, 5.0 m and F = 6.0
Last, 5.0 m and F decreases uniformly from 6.0 N to zero
What was the total work done by this force during the full 20-m trip?

A) 15 J
B) 30 J
C) 45 J
D) 60 J
E) 75 J

Question 29

Use the figure to answer the question. The graph shows the speed of a light truck of mass 4000 kg coasting on neutral down a level straight road. The truck is slowing down due to air resistance and rolling friction.
The net force at 25s is ____ the net force at 5s.

A) less than
B) equal to
C) greater than
D) unable to tell
E) depends on what the acceleration is

Question 30

Use the figure to answer the question. The graph shows the speed of a light truck of mass 4000 kg coasting on neutral down a level straight road. The truck is slowing down due to air resistance and rolling friction.
A vertical light spring stretches a distance h meters when a mass m is hung from it. The spring/mass system is now placed on a horizontal frictionless table and set into oscillation with amplitude h and maximum velocity v. What is the total energy involved in the spring/mass oscillating system.

A) kh² + mv²
B) kh² + mgh
C) mv² + mgh²
D) mgh + kh² + mv²
E) mv²

Question 31

The graph represents the force acting on a body plotted against the displacement of the body in the direction of the force. The total work done by the force from x = 0 to x = x is

A) m
B) mx² + b
C) ·mx² + b
D) mx + b
E) ·mx² + bx

Question 32

The angle between the vectors = -2 + 3 and = 4 - 5 is approximately

A) 5º
B) 47º
C) 175º
D) 15º
E) 26º

Question 33

In pushing a load, a woman exerts a force as given by the graph. What was the total work done by the woman?

A) 400 J
B) 200 J
C) 2000 J
D) 1000 J
E) 500 J

Question 34

A donkey is attached by a rope to a wooden cart at an angle of 23 ^$\circ$ to the horizontal. The tension in the rope is 210 N. If the cart is dragged horizontally along the floor with a constant speed of 6 km/h, calculate how much work the donkey does in 35 minutes.

A) 740 kJ
B) 290 kJ
C) 680 kJ
D) 11 kJ
E) 0.70 kJ

Question 35

If vector = -2 + 3 and a vector = 4 - 5 , the inner product · is

A) -23
B) 7
C) -7
D) 23
E) 17

Question 36

Use the figure to answer the question. The graph shows the speed of a light truck of mass 4000 kg coasting on neutral down a level straight road. The truck is slowing down due to air resistance and rolling friction.
Suppose the driver decides to put the truck in gear and steps on the accelerator at 5s. What is the power needed to maintain the speed at 5s?

A) 20 kW
B) 40 kW
C) 60 kW
D) 80 kW
E) 100 kW

Question 37

A motorcycle of mass m starting from rest can attain a speed v after work W is performed by its engine. If the engine could perform work 4W then the final speed would be?

A) 4v
B) 2v
C) 16v
D) (2v)^1/2
E) (4v)^1/2

Question 38

What is the difference in work needed to push a 100 kg crate (at constant speed) a distance of 2 m along an inclined plane that is at an angle of 20 degrees with the horizontal, if the coefficient of kinetic friction was equal to 0.20 or zero?

A) 670 N
B) 1040 N
C) no difference
D) 370 N
E) 134 N

Question 39

You release an object from rest at a high altitude. If air resistance is considered, the curve that best represents the kinetic energy of the body as a function of the distance fallen is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 40

Kids love to crash their toy cars together. One such collision involves a 0.5 kg car moving at 0.3 m/s colliding with a stationary toy car of mass 0.3 kg. The two toys stick together and move away from the collision point at 0.188 m/s. By what factor is the initial kinetic energy greater than the final kinetic energy?

A) 0.63
B) 1.6
C) 2.5
D) 4.2
E) 1.0 The kinetic energy stays the same.

Question 41

A 50% efficient hydroelectric power plant generates electricity from water falling a height of 110 m and at a rate of x kg/s. If the maximum possible power output of the plant was 27.0 MW, what is x?

A) 25,000 kg/s
B) 50,000 kg/s
C) 100,000 kg/s
D) 5100 kg/s
E) 510,000 kg/s

Question 42

To maintain an automobile in approximately constant acceleration, its engine must develop power that increases with time. Suppose that in one situation the work done by an engine is given by
W = 7000t² + 40,000t + 100,000
Where the units are SI. The power developed by this engine at t = 2 s is

A) 3.4 $\times$ 10⁴ W
B) 6.8 $\times$ 10⁴ W
C) 1.0 $\times$ 10⁵ W
D) 2.1 $\times$ 10⁵ W
E) 3.0 $\times$ 10⁵ W

Question 43

The power developed by a certain engine is a function of time according to
P = 2 + 2t + 3t²
Where the units are SI. The work done by the engine in the interval from t = 0 to t = 2 s is

A) 9 J
B) 10 J
C) 14 J
D) 16 J
E) 18 J

Question 44

Power P is required to do work W in time interval t. What power is required to do work 3W in time interval 5t?

A) P
B) 3P
C) 5P
D) 5P/3
E) 3P/5

Question 45

A motor develops power as shown in the graph. The energy expended by the motor in the time interval between t = 10 s and t = 30 s is

A) 1.0 J
B) 1.3 J
C) 0.20 kJ
D) 0.60 kJ
E) 0.70 kJ

Question 46

Determine which of the following statements is correct.

A) The scalar product of two vectors can be negative.
B) where c is a constant.
C) The scalar product can be non-zero even if two of the three components of the two vectors are equal to zero.
D) If then .
E) All the above statements are correct.

Question 47

A motor is lifting a mass of 35.0 kg at a constant speed of 6.00 m/s. If friction is neglected, the power developed by the motor to do this lifting is

A) 740 W
B) 1.5 $\times$ 10³ W
C) 2.1 $\times$ 10³ W
D) 59 W
E) 43 W

Question 48

A 5-kg object undergoes a displacement $\Delta$
= 2 + 3 . During the displacement, a constant force = 4 - 2 acts on the object. All values are given in SI units. The work done by the force on this object is

A) 8 J
B) -6 J
C) 2 J
D) 14 J
E) -2 J

Question 49

An electrical appliance expends energy as shown in the graph. The power developed in the appliance between t = 15 s and t = 25 s is

A) 0.34 kW
B) 0.11 kW
C) 20 W
D) 1.3 kW
E) 1.0 W

Question 50

The angle between the vector = + 2 + 3 and the y axis is approximately

A) 58º
B) 75º
C) 17º
D) 26º
E) 37º

Question 51

If a fighter jet doubles its speed, by what factor should the power from the engine change?

A) by half
B) unchanged
C) doubled
D) quadrupled
E) 8 times

Question 52

Consider two engines. The larger is rated at 2 W and the smaller at 1 W. The smaller one can do a certain quantity of work in 2 h. The larger can do twice as much work in a time of

A) 30 min
B) 1 h
C) 2 h
D) 4 h
E) 1.4 h

Question 53

A force acts on a body and produces an acceleration . The body undergoes a displacement and attains a velocity in time t. The instantaneous power being developed at time t is given by

A) ·
B) · at²
C) ·
D) ( · 2 ) /t²
E) ·

Question 54

The work done by a crane lifting a boat is plotted on the graph. The power developed by the crane when t = 1.5 s is

A) 40 W
B) 20 W
C) 10 W
D) 27 W
E) 30 W

Question 55

A body is acted upon by a force of 10 N and undergoes displacement in the direction of the force in accordance with the relation
S = 3t² + 2t
Where the units are SI. The rate at which the force is doing work at the instant t = 2 s is

A) 14 W
B) 12 W
C) 120 W
D) 140 W
E) 160 W

Question 56

Power P is required to lift a body a distance d at a constant speed v. What power is required to lift the body a distance 2d at constant speed 3v?

A) P
B) 2P
C) 3P
D) 6P
E) 3P/2

Question 57

A body is acted upon by a force of 10 N and undergoes a displacement in the direction of the force in accordance with the relation s = 3t² + 2t, where s is the displacement in meters and t is in seconds. The rate at which the force is doing work at the instant t = 2 s is

A) 14 W
B) 12 W
C) 120 W
D) 140 W
E) 160 W

Question 58

As a punishment for being late to a practice session the coach orders her star athlete to run up the stadium steps. The player's mass is 80 kg and it takes one minute for her to run up the 120 steps at a constant rate. If each step is of height 0.5 m, what is the power output of the player?

A) 80.0 W
B) 13.0 W
C) 1570 W
D) 785 W
E) 390 W

Question 59

What is the power output needed from a motor to lift, in the absence of friction, a mass of 1.5 $\times$ 10⁴ kg 25 m in 6.0 s at constant speed?

A) 2.0 $\times$ 10⁶ W
B) 6.1 $\times$ 10⁵ W
C) 2.2 $\times$ 10⁴ W
D) 8.3 $\times$ 10⁵ W
E) 3.1 $\times$ 10⁵ W

Question 60

The object in the figure has a mass of 3.45 kg and is pulled up a slope AB, which is 36 m long; the height BC is 3.00 m. There is no friction and the acceleration is constant. The speed v₁ at A is 3.5 m/s whereas the speed v₂ at B is 5.5 m/s. The average power developed by the motor pulling the object is

A) 17 W
B) 3.9 W
C) 13 W
D) 0.13 kW
E) 43 W

Question 61

A skier of mass 50 kg is moving at speed 10 m/s at point P₁ down a ski slope with negligible friction. What is the skier's kinetic energy when she is at point P₂, 20 m below P₁?

A) 2500 J
B) 9800 J
C) 12300 J
D) 13100 J
E) 15000 J

Question 62

Two skiers start at the same place and finish at the same place. Skier A takes a straight, smooth route to the finish whereas Skier B takes a curvy, bumpy route to the finish. If you assume that friction is negligible, which of the following statements is true?

A) Skier A has the same speed as skier B at the finish.
B) Skier B has the greater speed at the finish.
C) Skier A has the greater speed at the finish because the route is straight.
D) Skier A has the greater speed at the finish because the route is smooth.
E) Skier A has the greater speed at the finish because the route is both straight and smooth.

Question 63

An object of mass, m, is placed in an arc of a circle of radius, r. The coefficient of kinetic friction between the object and the surface of the arc is $\mu$ _k. What is the work done by friction in going from P₁ and P₂?

A) - $\mu$ _kmg r (cos( $\theta$ ₂)-cos( $\theta$ ₁))
B) - $\mu$ _kmg r (sin( $\theta$ ₂)-sin( $\theta$ ₁))
C) - $\mu$ _kmg r cos( $\theta$ ₂) sin( $\theta$ ₁)
D) - $\mu$ _kmg r sin(F $\theta$ ₂)cos( $\theta$ ₁)
E) none of the above

Question 64

A hydroelectric power plant generates electricity from water falling a height of h m and at a rate of 20,000 kg/s. If the theoretical maximum power output of the plant is 15.0 MW what is the height h?

A) 750 m
B) 153 m
C) 102 m
D) 76.5 m
E) 38.3 m

Question 65

What minimum power rating must a water pump have if needs to raise water at 20 kg per minute from a depth of 9 m?

A) 1.76 kW
B) 29.4 W
C) 106 kW
D) 3.0 W
E) 180 W

Question 66

The human heart is essentially a pump for moving blood around the body. If its average power output (over many beats) is about 2.0 W and it pumps blood at an overall average speed of 0.3 m/s into the output aorta channel, calculate the average force with which the heart moves the blood into the aorta.

A) 0.60 N
B) 6.7 N
C) 22 N
D) 66 N
E) 0.18 N

Question 67

Egyptian pyramid workers push a 1200-kg block up an incline that has an angle of 69 degrees to the vertical, at a constant speed of 0.5 m/s. The coefficient of kinetic friction between the block and the incline surface is 0.44. How much power must the workers supply?

A) 3.1 $\times$ 10² W
B) 9.3 kW
C) 4.5 kW
D) 7.9 kW
E) 2.4 kW

Question 68

If the average power output of a car engine is the same as a 100-W light bulb, how long would it take a 1200-kg car to go from zero to 96 km/h (60 mph)?

A) 8.5 $\times$ 10³ s
B) 5.5 $\times$ 10⁴ s
C) 65 s
D) 160 s
E) 4.3 $\times$ 10³ s

Question 69

A Blackhawk helicopter is winching up an injured soldier from a danger zone. The soldier and his kit have a mass of 150 kg and are pulled up 50 m in the air at a steady rate. If it takes 30 s to pull the soldier up, how much power has been used by the helicopter's 65% efficient winch engine?

A) 2.5 kW
B) 3.8 kW
C) 1.6 kW
D) 4.1 kW
E) 3.2 kW

Question 70

A 6.0-kg block slides from point A down a frictionless curve to point B. After the block passes point B, a friction force opposes the motion of the block so that it comes to a stop 2.5 m from B. Calculate the coefficient of kinetic friction between the block and the surface after position B.

A) 2.5
B) 0.40
C) >0.40
D) 0.40 N
E) 2.5 N

Question 71

A 6.0-kg block slides from rest at position A down a frictionless incline to position B. The speed of the block at B is

A) 3.1 m/s
B) 4.4 m/s
C) 11 m/s
D) 1.8 m/s
E) 20 m/s