Deck 6: Work, Force and Energy

Question 1

A block is pushed across a rough horizontal surface from point A to point B by a force (magnitude P = 5.4 N) as shown in the figure. The magnitude of the force of friction acting on the block between A and B is 1.2 N and points A and B are 0.5 m apart. If the kinetic energies of the block at A and B are 4.0 J and 5.6 J, respectively, how much work is done on the block by the force P between A and B?

A)2.7 J
B)1.0 J
C)2.2 J
D)1.6 J
E)3.2 J

Answer 1

2.2 J

Question 2

A 2.5-kg object falls vertically downward in a viscous medium at a constant speed of 2.5 m/s. How much work is done by the force the viscous medium exerts on the object as it falls 80 cm?

A)+2.0 J
B)+20 J
C)(-2.0 J)
D)(-20 J)
E)+40 J

Answer 2

(-20 J)

Question 3

The horizontal surface on which the block slides is frictionless. The speed of the block before it touches the spring is 6.0 m/s. How fast is the block moving at the instant the spring has been compressed 15 cm? k = 2.0 kN/m

A)3.7 m/s
B)4.4 m/s
C)4.9 m/s
D)5.4 m/s
E)14 m/s

Answer 3

3.7 m/s

Question 4

A force acting on an object moving along the x axis is given by Fx = (14x - 3.0x2) N where x is in m. How much work is done by this force as the object moves from x = -1 m to x = +2 m?

A)+12 J
B)+28 J
C)+40 J
D)+42 J
E)(-28 J)

Question 5

A 1.5-kg object moving along the x axis has a velocity of +4.0 m/s at x = 0. If the only force acting on this object is shown in the figure, what is the kinetic energy of the object at x = +3.0 m?

A)18 J
B)21 J
C)23 J
D)26 J
E)8 J

Question 6

A 4.0-kg block is lowered down a 37 $\degree$ incline a distance of 5.0 m from point A to point B. A horizontal force (F = 10 N) is applied to the block between A and B as shown in the figure. The kinetic energy of the block at A is 10 J and at B it is 20 J. How much work is done on the block by the force of friction between A and B?

A)(-58 J)
B)(-53 J)
C)(-68 J)
D)(-63 J)
E)(-47 J)

Question 7

The only force acting on a 2.0-kg body moving along the x axis is given by Fx = (2.0x) N, where x is in m. If the velocity of the object at x = 0 is +3.0 m/s, how fast is it moving at x = 2.0 m?

A)4.2 m/s
B)3.6 m/s
C)5.0 m/s
D)5.8 m/s
E)2.8 m/s

Question 8

How much work is done by a person lifting a 2.0-kg object from the bottom of a well at a constant speed of 2.0 m/s for 5.0 s?

A)0.22 kJ
B)0.20 kJ
C)0.24 kJ
D)0.27 kJ
E)0.31 kJ

Question 9

A block slides on a rough horizontal surface from point A to point B. A force (magnitude P = 2.0 N) acts on the block between A and B, as shown. Points A and B are 1.5 m apart. If the kinetic energies of the block at A and B are 5.0 J and 4.0 J, respectively, how much work is done on the block by the force of friction as the block moves from A to B?

A)(-3.3 J)
B)+1.3 J
C)+3.3 J
D)(-1.3 J)
E)+4.6 J

Question 10

An object moving along the x axis is acted upon by a force Fx that varies with position as shown. How much work is done by this force as the object moves from x = 2 m to x = 8 m?

A)(-10 J)
B)+10 J
C)+30 J
D)(-30 J)
E)+40 J

Question 11

A body moving along the x axis is acted upon by a force Fx that varies with x as shown. How much work is done by this force as the object moves from x = 1 m to x = 8 m?

A)(-2 J)
B)(-18 J)
C)(-10 J)
D)(-26 J)
E)+18 J

Question 12

A 2.0-kg projectile moves from its initial position to a point that is displaced 20 m horizontally and 15 m above its initial position. How much work is done by the gravitational force on the projectile?

A)+0.29 kJ
B)(-0.29 kJ)
C)+30 J
D)(-30 J)
E)(-50 J)

Question 13

A 2.0-kg body moving along the x axis has a velocity vx = 5.0 m/s at x = 0. The only force acting on the object is given by Fx = (-4.0x) N, where x is in m. For what value of x will this object first come (momentarily) to rest?

A)4.2 m
B)3.5 m
C)5.3 m
D)6.4 m
E)5.0 m

Question 14

A 2.0-kg block slides down a frictionless incline from point A to point B. A force (magnitude P = 3.0 N) acts on the block between A and B, as shown. Points A and B are 2.0 m apart. If the kinetic energy of the block at A is 10 J, what is the kinetic energy of the block at B?

A)27 J
B)20 J
C)24 J
D)17 J
E)37 J

Question 15

If the resultant force acting on a 2.0-kg object is equal to $(3 \tilde{\mathbf{i}}+4 \tilde{\mathbf{j}})$ N, what is the change in kinetic energy as the object moves from $(7 \tilde{\mathbf{i}}-8 \tilde{\mathbf{j}})$ m to $(11 \tilde{\mathbf{i}}-5 \tilde{\mathbf{j}})$ m?

A)+36 J
B)+28 J
C)+32 J
D)+24 J
E)+60 J

Question 16

A 3.0-kg block is dragged over a rough horizontal surface by a constant force of 16 N acting at an angle of 37 $\degree$ above the horizontal as shown. The speed of the block increases from 4.0 m/s to 6.0 m/s in a displacement of 5.0 m. What work was done by the friction force during this displacement?

A)(-34 J)
B)(-64 J)
C)(-30 J)
D)(-94 J)
E)+64 J

Question 17

A 2.0-kg block sliding on a frictionless horizontal surface is attached to one end of a horizontal spring (k = 600 N/m) which has its other end fixed. The speed of the block when the spring is extended 20 cm is equal to 3.0 m/s. What is the maximum speed of this block as it oscillates?

A)4.6 m/s
B)5.3 m/s
C)5.7 m/s
D)4.9 m/s
E)3.5 m/s

Question 18

The only force acting on a 1.8-kg body as it moves along the x axis is given by Fx = -(3.0x) N, where x is in m. If the velocity of the body at x = 0 is vx = +8.0 m/s, at what value of x will the body have a velocity of +4.0 m/s?

A)5.7 m
B)5.4 m
C)4.8 m
D)4.1 m
E)6.6 m

Question 19

A 2.0-kg block situated on a frictionless incline is connected to a light spring (k = 100 N/m), as shown. The block is released from rest when the spring is unstretched. The pulley is frictionless and has negligible mass. What is the speed of the block when it has moved 0.20 m down the plane?

A)76 cm/s
B)68 cm/s
C)60 cm/s
D)82 cm/s
E)57 cm/s

Question 20

A 10-kg block on a horizontal frictionless surface is attached to a light spring (force constant = 0.80 kN/m). The block is initially at rest at its equilibrium position when a force (magnitude P = 80 N) acting parallel to the surface is applied to the block, as shown. What is the speed of the block when it is 13 cm from its equilibrium position?

A)0.85 m/s
B)0.89 m/s
C)0.77 m/s
D)0.64 m/s
E)0.52 m/s

Question 21

Two clowns are launched from the same spring-loaded circus cannon with the spring compressed the same distance each time. Clown A has a 40-kg mass; clown B a 60-kg mass. The relation between their kinetic energies at the instant of launch is:

A) $K_{A}=\frac{3}{2} K_{B}$ .
B) $K_{A}=\sqrt{\frac{3}{2}} K_{B}$ .
C)KA = KB.
D) $K_{B}=\sqrt{\frac{3}{2}} K_{A}$ .
E) $K_{B}=\frac{3}{2} K_{A}$ .

Question 22

Carts A and B have equal masses and travel equal distances D on side-by-side straight frictionless tracks while a constant force F acts on A and a constant force 2F acts on B. Both carts start from rest. The velocities $\overrightarrow{\mathbf{v}}$ A and $\overrightarrow{\mathbf{v}}$ B of the bodies at the end of distance D are related by:

A) $\overrightarrow{\mathbf{v}}$ B = $\overrightarrow{\mathbf{v}}$ A .
B) $\overrightarrow{\mathbf{v}}$ B = $\sqrt{2}$
$\overrightarrow{\mathbf{v}}$ A.
C) $\overrightarrow{\mathbf{v}}$ B = 2 $\overrightarrow{\mathbf{v}}$ A.
D) $\overrightarrow{\mathbf{v}}$ B = 4 $\overrightarrow{\mathbf{v}}$ A.
E) $\overrightarrow{\mathbf{v}}$ A = 2 $\overrightarrow{\mathbf{v}}$ B.

Question 23

The equation below is the solution to a physics problem: $\frac{1}{2}(2.30 \mathrm{~kg})\left(3.90 \frac{\mathrm{~m}}{\mathrm{~s}}\right)^{2}=\frac{1}{2}(2.30 \mathrm{~kg})\left(2.33 \frac{\mathrm{~m}}{\mathrm{~s}}\right)^{2}+(2.30 \mathrm{~kg})\left(9.80 \frac{\mathrm{~m}}{\mathrm{~s}^{2}}\right)(1.00 \mathrm{~m}) \cos \left(60^{\circ}\right)$ .The most likely physical situation it describes is:

A)a 2.30 kg cart rolling up a 30 $\degree$ incline.
B)a 2.30 kg cart rolling down a 30 $\degree$ incline.
C)a 2.30 kg cart rolling up a 60 $\degree$ incline.
D)a 2.30 kg cart rolling down a 60 $\degree$ incline.
E)a 2.30 kg cart rolling down a 90 $\degree$ incline.

Question 24

Two balls, A and B, of mass m and 2m respectively, are carried to height h at constant velocity, but B rises twice as fast as A. The work the gravitational force does on B is:

A)one quarter the work done on A.
B)one half the work done on A.
C)the same as the work done on A.
D)twice the work done on A.
E)four times the work done on A.

Question 25

In a contest, two tractors pull two identical blocks of stone the same distance over identical surfaces. However, block A is moving twice as fast as block B when it crosses the finish line. Which statement is correct?

A)Block A has twice as much kinetic energy as block B.
B)Block B has lost twice as much kinetic energy to friction as block A.
C)Block B has lost twice as much kinetic energy as block A.
D)Both blocks have had equal losses of energy to friction.
E)No energy is lost to friction because the ground has no displacement.

Question 26

Positive work can be done:

A)by friction on the tyres when a car is accelerating without skidding.
B)by a spring when it launches a clown in the air.
C)by a hand throwing a ball.
D)by all of the above.
E)only by (b) and (c) above.

Question 27

Planets go around the sun in elliptical orbits. The highly exaggerated diagram below shows a portion of such an orbit and the force on the planet at one position along that orbit. The planet is moving to the right. F|| and $F_{\perp}$ are the components of the force parallel (tangential) and perpendicular (normal) to the orbit. The work they do is W|| and $W_{\perp}$ . At the position shown:

A)W|| slows the planet down; $W_{\perp}$ speeds it up.
B)W|| slows the planet down; $W_{\perp}$ does no work on it.
C)W|| speeds the planet up; $W_{\perp}$ does no work on it.
D)W|| speeds the planet up; $W_{\perp}$ slows it down.
E)W|| does no work on it; $W_{\perp}$ speeds the planet up.

Question 28

The same constant force is used to accelerate two carts of the same mass, initially at rest, on horizontal frictionless tracks. The force is applied to cart A for twice as long a time as it is applied to cart B. The work the force does on A is WA; that on B is WB. Which statement is correct?

A)WA = WB.
B)WA = $\sqrt{2}$ WB.
C)WA = 2 WB.
D)WA = 4 WB.
E)WB = 2 WA.

Question 29

Carts A and B have equal masses and travel equal distances on straight frictionless tracks while a constant force F is applied to A, and a constant force 2F is applied to B. The relative amounts of work done by the two forces are related by:

A)WA = 4 WB.
B)WA = 2 WB.
C)WA = WB.
D)WB = 2 WA.
E)WB = 4 WA.

Question 30

Negative work can be done:

A)by friction on the tyres while a car is accelerating without skidding.
B)by a spring at the bottom of an elevator shaft when it stops a falling elevator.
C)by a hand catching a ball.
D)by all of the above.
E)only by (b) and (c) above.

Question 31

Two identical springs with spring constant 50 N/m support a 5.0 N weight as in the picture below. What is the change in length of each spring when the weight is hung on the springs?

A)2.9 cm
B)5.0 cm
C)5.8 cm
D)7.5 cm
E)10.0 cm

Question 32

The graph below shows how the force on a 0.500 kg particle varies with position. If the particle has speed $v=2.23 \frac{\mathrm{~m}}{\mathrm{~s}}$ at x = 0.00 m, what is its speed in m/s when x = 8.00 m?

A)2.00
B)10.7
C)14.8
D)15.0
E)21.1

Question 33

A 30-kg child sitting 5.0 m from the centre of a merry-go-round has a constant speed of 5.0 m/s. While she remains seated in the same spot and travels in a circle, the work the seat performs on her in one complete rotation is:

A)0 J.
B)150 J.
C)1500 J.
D)4700 J.
E)46 000 J.

Question 34

The force of static friction exerted on an automobile's tyres by the ground:

A)provides the accelerating force that makes the car move forward.
B)does positive work on the car while it is accelerating.
C)does negative work on the car while it is decelerating.
D)does everything listed in (a), (b) and (c).
E)only does positive or negative work as in (b) or (c).

Question 35

After a skydiver reaches terminal velocity:

A)the force of gravity no longer performs work on the skydiver.
B)work performed by the force of gravity is converted into gravitational potential energy.
C)gravitational potential energy is no longer available to the system of the skydiver plus the Earth.
D)gravitational potential energy is converted into thermal energy.
E)thermal energy is converted into gravitational potential energy.

Question 36

Equal amounts of work are performed on two bodies, A and B, initially at rest, and of masses m and 2m respectively. The relation between their speeds immediately after the work has been done on them is:

A)vA = $\sqrt{2}$ vB.
B)vA = 2vB.
C)vA = vB.
D)vB = $\sqrt{2}$ vA.
E)vB = 2vA.

Question 37

A group of rioting students throw rotten eggs at some passing politicians. Two eggs of equal mass are thrown with equal velocity. Egg B hits the soft padded shoulders of a politician's suit but egg A misses and hits the building wall behind them instead. Compare the work done on the eggs in reducing their velocities to zero.

A)More work was done on A than on B.
B)More work was done on B than on A.
C)The amount of work is the same for both.
D)It is meaningless to compare the amount of work because the forces were so different.
E)Work was done on B, but no work was done on A because the wall did not move.

Question 38

Two cannonballs are dropped from a second floor physics lab at height h above the ground. Ball B has four times the mass of ball A. When the balls pass the bottom of a first floor window at height $\frac{h}{4}$ above the ground, the relation between their kinetic energies, KA and KB, is:

A)KA = 4KB.
B)KA = 2KB.
C)KA = KB.
D)KB = 2KA.
E)KB = 4KA.

Question 39

The work $\overrightarrow{\mathbf{F}}_{s p} \cdot d \overrightarrow{\mathbf{x}}$ done by the force exerted by the spring on a mass attached to the end of the spring when the mass has displacement d $\overrightarrow{\mathbf{x}}$ is

A)always negative.
B)always positive.
C)negative half the time, positive the other half of the time.
D)positive more than it is negative.
E)negative more than it is positive.

Question 40

Sally, who weighs 450 N, stands on a skate board while Roger pushes it forward 13.0 m at constant velocity on a level straight street. He applies a constant 100 N force.

A)The work Roger does on the skateboard is 0 J.
B)The work Roger does on the skateboard is 1300 J.
C)The work Sally does on the skateboard is 1300 J.
D)The work Sally does on the skateboard is 5850 J.
E)The work Roger does on the skateboard is 5850 J.

Question 41

A champion athlete can produce one horsepower (746 W) for a short period of time. If a 70-kg athlete were to bicycle to the summit of a 500-m high mountain while expending power at this rate, she would reach the summit in ____ seconds.

A)1
B)460
C)500
D)1000
E)35 000

Question 42

A cricket ball is thrown and lands 120 m away. While the ball is in flight, assuming the effect of air friction is negligible, which of the following is true?

A)At maximum height the ball has its greatest kinetic energy.
B)The horizontal component of the ball's kinetic energy is constant.
C)The vertical component of the ball's kinetic energy is constant.
D)The mechanical energy of the ball is greater when nearer to the ground.
E)No answer above is correct.

Question 43

For the potential $U=2 x^{2}-8 x$ , find the stable equilibrium point, if any.

Question 44

While running, a person dissipates about 0.6 J of mechanical energy per step per kilogram of body mass. If a 60-kg person runs with a power of 70 Watts during a race, how fast is the person running? Assume a running step is 1.5 m long.

Question 45

A particle is subject to the potential $U=2 x^{2} y+6 y$ . What is the value of the y component of the force on the particle at the point (x, y) = (2.0, 3.0)?

A)24
B)(-24)
C)14
D)(-14)
E)28

Question 46

When an automobile moves with constant velocity the power developed is used to overcome the frictional forces exerted by the air and the road. If the power developed in an engine is 50.0 hp, what total frictional force acts on the car at 55 mph (24.6 m/s)? One horsepower equals 746 W.