Deck 7: Conservation of Energy

Question 1

A block (mass = 4.0 kg) sliding on a horizontal frictionless surface is attached to one end of a horizontal spring (k = 100 N/m) which has its other end fixed. If the maximum distance the block slides from the equilibrium position is equal to 20 cm, what is the speed of the block at an instant when it is a distance of 16 cm from the equilibrium position?

A)71 cm/s
B)60 cm/s
C)80 cm/s
D)87 cm/s
E)57 cm/s

Answer 1

60 cm/s

Question 2

A 12-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)0.78 m/s
B)0.81 m/s
C)0.71 m/s
D)0.58 m/s
E)0.64 m/s

Answer 2

0.78 m/s

Question 3

A 0.60-kg object is suspended from the ceiling at the end of a 2.0-m string. When pulled to the side and released, it has a speed of 4.0 m/s at the lowest point of its path. What maximum angle does the string make with the vertical as the object swings up?

A)61 $\degree$
B)54 $\degree$
C)69 $\degree$
D)77 $\degree$
E)47 $\degree$

Answer 3

54 $\degree$

Question 4

A 3.0-kg mass is dropped from the edge of a 50-m tall building with an initial speed of zero. The mass strikes the ground with a downward velocity of 25 m/s. Find the change in mechanical energy of the mass caused by air resistance between the point where it is dropped and the point where it strikes the ground?

A)(-0.46 kJ)
B)(-0.53 kJ)
C)(-0.61 kJ)
D)(-0.38 kJ)
E)(-0.81 kJ)

Question 5

A 10-kg object is dropped from rest. After falling a distance of 50 m, it has a speed of 26 m/s. What is the change in mechanical energy caused by the dissipative (air) resistive force on the object during this descent?

A)(-1.3 kJ)
B)(-1.5 kJ)
C)(-1.8 kJ)
D)(-2.0 kJ)
E)(-2.3 kJ)

Question 6

The two masses in the figure are released from rest. After the 3.0-kg mass has fallen 1.5 m, it is moving with a speed of 3.8 m/s. What is the change in mechanical energy done on the system during this time interval by the frictional force on the 2.0 kg mass?

A)(-12 J)
B)(-17 J)
C)(-20 J)
D)(-8.0 J)
E)(-28 J)

Question 7

A spring (k = 200 N/m) is suspended with its upper end supported from a ceiling. With the spring hanging in its equilibrium configuration, an object (mass = 2.0 kg) is attached to the lower end and released from rest. What is the speed of the object after it has fallen 4.0 cm?

A)90 cm/s
B)79 cm/s
C)96 cm/s
D)83 cm/s
E)57 cm/s

Question 8

A 2.0-kg block slides down a fixed, rough curved track. The block has a speed of 5.0 m/s after its height above a horizontal surface has decreased by 1.8 m. Assume the block starts from rest. What is the change in mechanical energy of the block caused by the force of friction during this descent?

A)(-14 J)
B)(-12 J)
C)(-10 J)
D)(-16 J)
E)(-25 J)

Question 9

A 0.80-kg object tied to the end of a 2.0-m string swings as a pendulum. At the lowest point of its swing, the object has a kinetic energy of 10 J. Determine the speed of the object at the instant when the string makes an angle of 50 $\degree$ with the vertical.

A)5.6 m/s
B)4.4 m/s
C)3.3 m/s
D)5.0 m/s
E)6.1 m/s

Question 10

A skier weighing 0.70 kN goes over a frictionless circular hill as shown. If the skier's speed at point A is 9.2 m/s, what is his speed at the top of the hill (point B)?

A)3.1 m/s
B)6.2 m/s
C)5.2 m/s
D)4.1 m/s
E)6.5 m/s

Question 11

A 0.04-kg ball is thrown from the top of a 30-m tall building (point A) at an unknown angle above the horizontal. As shown in the figure, the ball attains a maximum height of 10 m above the top of the building before striking the ground at point B. If air resistance is negligible, what is the value of the kinetic energy of the ball at B minus the kinetic energy of the ball at A (KB - KA)?

A)12 J
B)(-12 J)
C)20 J
D)(-20 J)
E)32 J

Question 12

A 1.2-kg mass is projected from ground level with a velocity of 30 m/s at some unknown angle above the horizontal. A short time after being projected, the mass barely clears a 16-m tall fence. Disregard air resistance and assume the ground is level. What is the kinetic energy of the mass as it clears the fence?

A)0.35 kJ
B)0.73 kJ
C)0.40 kJ
D)0.68 kJ
E)0.19 kJ

Question 13

A particle is acted upon by only two forces, one conservative and one non-conservative and neither being a force of friction, as it moves from point A to point B. The kinetic energies of the particle at points A and B are equal if:

A)the sum of the works of the two forces is zero.
B)the work of the conservative force is equal to the work of the non-conservative force.
C)the work of the conservative force is zero.
D)the work of the non-conservative force is zero.
E)None of the above.

Question 14

A spring (k = 600 N/m) is placed in a vertical position with its lower end supported by a horizontal surface. The upper end is depressed 20 cm, and a 4.0-kg block is placed on top of the depressed spring. The system is then released from rest. How far above the point of release will the block rise?

A)46 cm
B)36 cm
C)41 cm
D)31 cm
E)20 cm

Question 15

In a given frictionless displacement of a particle, its kinetic energy increases by 25 J while its potential energy decreases by 10 J. Determine the work of the non-conservative forces acting on the particle during this displacement.

A)(-15 J)
B)+35 J
C)+15 J
D)(-35 J)
E)+55 J

Question 16

A 25-kg block on a horizontal surface is attached to a light spring (force constant = 8.0 kN/m). The block is pulled 10 cm to the right from its equilibrium position and released from rest. When the block has moved 2.0 cm toward its equilibrium position, its kinetic energy is 12 J. What is the change in mechanical energy caused by the frictional force on the block as it moves the 2.0 cm?

A)(-4.0 J)
B)(-3.5 J)
C)(-2.4 J)
D)(-2.9 J)
E)(-15 J)

Question 17

A single conservative force Fx = (6.0x - 12) N (x is in m) acts on a particle moving along the x axis. The potential energy associated with this force is assigned a value of +20 J at x = 0. What is the potential energy at x = 3.0 m?

A)+11 J
B)+29 J
C)+9.0 J
D)(-9.0 J)
E)+20 J

Question 18

A 20-kg mass is fastened to a light spring (k = 380 N/m) that passes over a pulley as shown. The pulley is frictionless, and the mass is released from rest when the spring is unstretched. After the mass has dropped 0.40 m, what is its speed?

A)2.2 m/s
B)2.5 m/s
C)1.9 m/s
D)1.5 m/s
E)3.6 m/s

Question 19

A spring (k = 600 N/m) is placed in a vertical position with its lower end supported by a horizontal surface. A 2.0-kg block that is initially 0.40 m above the upper end of the spring is dropped from rest onto the spring. What is the kinetic energy of the block at the instant it has fallen 0.50 m (compressing the spring 0.10 m)?

A)5.3 J
B)6.8 J
C)6.3 J
D)5.8 J
E)6.5 J

Question 20

A 1.2-kg mass is projected down a rough circular track (radius = 2.0 m) as shown. The speed of the mass at point A is 3.2 m/s, and at point B, it is 6.0 m/s. What is the change in mechanical energy done on the system between A and B by the force of friction?

A)(-8.9 J)
B)(-7.3 J)
C)(-8.1 J)
D)(-6.6 J)
E)(-24 J)

Question 21

A spring with spring constant 800 N/m compressed 0.200 m is released and projects a 0.800 kg mass along a frictionless surface. The mass reaches a surface area where $\mu$ k = 0.400 and comes to a stop. The following student solution contains at least one error. What is the error? $\frac{1}{2}\left(800 \frac{\mathrm{~N}}{\mathrm{~m}}\right)(0.200 \mathrm{~m})^{2}=\frac{1}{2}(0.500 \mathrm{~kg})\left(8.00 \frac{\mathrm{~m}}{\mathrm{~s}}\right)^{2}+0.400(0.500 \mathrm{~kg})\left(9.80 \frac{\mathrm{~m}}{\mathrm{~s}^{2}}\right)(8.16 \mathrm{~m})$

A)The elastic potential energy is equal only to the kinetic energy on the right, and is never equal to the internal thermal energy.
B)The elastic potential energy is equal only to the internal thermal energy on the right, and is never equal to the kinetic energy.
C)The elastic potential energy is equal to either the kinetic energy or the internal thermal energy on the right, but not to their sum, depending on the part of the problem being done.
D)Elastic potential energy cannot end up as internal energy change caused by friction.
E)Change in mechanical energy by friction cannot end up as elastic potential energy.

Question 22

Identical masses m are attached to identical springs of spring constant k suspended from the ceiling. With both masses hanging in their equilibrium positions, mass A is pulled down 10 cm and released while mass B is pushed up 10 cm and released. Which statement is correct?

A)Mass A will travel a smaller distance to its highest point than mass B will travel to its lowest point.
B)Mass A will travel a greater distance to its highest point than mass B will travel to its lowest point.
C)Masses A and B will travel equal distances between their highest and lowest points.
D)More work was done on mass A by the extending force than on mass B by the compressing force.
E)The total work done on mass A by the extending force was equal to the total work done on mass B by the compressing force.

Question 23

Two equal masses are raised at constant velocity by ropes that run over pulleys, as shown below. Mass B is raised twice as fast as mass A. The magnitudes of the forces are FA and FB, while the power supplied is respectively PA and PB. Which statement is correct?

A)FB = FA; PB = PA.
B)FB = FA; PB = 2 PA.
C)FB = 2 FA; PB = PA.
D)FB = 2 FA; PB = 2 PA.
E)PA = FA; PB = FB.

Question 24

A large spring is used to stop the cars after they come down the last hill of a roller coaster. The cars start at rest at the top of the hill and are caught by a mechanism at the instant their velocities at the bottom are zero. Compare the compression of the spring, xA, for a fully loaded car with that, xB, for a lightly loaded car when mA = 2mB.

A)xA = $\frac{1}{2}$ xB.
B)xA = xB.
C)xA = $\sqrt{2}$ xB.
D)xA = 2 xB.
E)xA = 4 xB.

Question 25

A pendulum bob has potential energy U0 when held taut in a horizontal position. The bob falls until it is 30 $\degree$ away from the horizontal position, when it has potential energy UA. It continues to fall until the string is vertical, when it has potential energy UB. Compare its potential energies at O, A, and B.

A)U0 = UA = UB.
B)UA- UB = 2U0.
C)UA - UB = U0 - UA.
D)U0 = UB = 2UA.
E)U0 - UA = 2(UA - UB).

Question 26

A 6.0-kg block slides along a horizontal surface. If µk = 0.20 for the block and surface, at what rate is the friction force changing the mechanical energy of the block at an instant when its speed is 4.0 m/s?

A)(-59 W)
B)(-47 W)
C)(-71 W)
D)(-82 W)
E)+71 W

Question 27

Two masses, MA and MB, with MB = 2MA, are released at the same time and allowed to fall straight down. Neglect air resistance. When we compare their kinetic energies after they have fallen for equal times, we find that

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

Question 28

Starting from rest at t = 0, a 5.0-kg block is pulled across a horizontal surface by a constant horizontal force having a magnitude of 12 N. If the coefficient of friction between the block and the surface is 0.20, at what rate is the 12-N force doing work at t = 5.0 s?

A)0.13 kW
B)0.14 kW
C)0.12 kW
D)26 W
E)12 W

Question 29

Which of the following is a conservative force? (All refer to a car on a slope.)

A)The force you exert on the car pushing it uphill.
B)The force exerted by rain drops falling on the car.
C)The frictional force of the road on the car.
D)The gravitational force acting on the car.
E)The force you exert on the car (pushing it uphill) after it starts to slide downhill.

Question 30

The equation below describes a physical situation: $\frac{1}{2}(1.70 \mathrm{~kg})\left(3.30 \frac{\mathrm{~m}}{\mathrm{~s}}\right)^{2}+(1.70 \mathrm{~kg})\left(9.80 \frac{\mathrm{~m}}{\mathrm{~s}^{2}}\right)(2.35 \mathrm{~m}) \sin 30^{\circ}$ $=\frac{1}{2}(1.70 \mathrm{~kg})\left(4.60 \frac{\mathrm{~m}}{\mathrm{~s}}\right)^{2}+0.320(1.70 \mathrm{~kg})\left(9.80 \frac{\mathrm{~m}}{\mathrm{~s}^{2}}\right)(2.35 \mathrm{~m}) \cos 30^{\circ}$ Which description best fits the equation?

A)A 1.70 kg block slows down while sliding down a frictionless plane inclined at a 30 $\degree$ angle.
B)A 1.70 kg block slows down while sliding down a plane with $\mu$ k = 0.320, with the plane inclined at a 30 $\degree$ angle.
C)A 1.70 kg block speeds up while sliding up a frictionless plane inclined at a 30 $\degree$ angle.
D)A 1.70 kg block speeds up while sliding down a plane with $\mu$ k = 0.320, with the plane inclined at a 30 $\degree$ angle.
E)A 1.70 kg block slides over the top of an inclined plane and then descends on the other side. Both planes, inclined at a 30 $\degree$ angle, have $\mu$ k = 0.320.

Question 31

A 3.50 kg block is pulled along a moving conveyor belt at a constant speed of 0.500 m/s relative to a stationary observer while the belt moves at a constant speed of 0.200 m/s in the opposite direction. If the coefficient of kinetic friction is 0.400, the magnitude of the mechanical energy dissipated, in J, caused by the force of friction on the block in 8.00 s is:

A)5.6.
B)22.0.
C)32.9.
D)54.8.
E)76.8.

Question 32

As a result of friction between internal parts of an isolated system:

A)the total mechanical energy of the system increases.
B)the total mechanical energy of the system decreases.
C)the total mechanical energy of the system remains the same.
D)the potential energy of the system increases but the kinetic energy remains the same.
E)the kinetic energy of the system increases but the potential energy of the system remains the same.

Question 33

A 2.0-kg block slides down a plane (inclined at 40 $\degree$ with the horizontal) at a constant speed of 5.0 m/s. At what rate is the gravitational force on the block doing work?

A)+98 W
B)+63 W
C)zero
D)+75 W
E)(-75 W)

Question 34

An astronaut tosses a ball out in space where gravitational forces may be neglected. What will happen to the ball?

A)It will stop as soon as the force the astronaut gave it is used up.
B)It will stop when the energy the astronaut gave it runs out.
C)It will stop after a short time because there is no gravity to keep it moving.
D)It will move in a circle like a boomerang.
E)It will be slowed down very gradually by collisions with molecules in space.

Question 35

Jane and Jake are looking at what happens to body 1 of mass m and body 2 of mass 2m, initially at rest, when equal forces are applied separately to the two bodies. Jake says that equal forces applied for equal times do equal amounts of work on the two bodies. Jane says that the two forces do equal amounts of work only if the two bodies move equal distances in the direction of the forces. Which one, if either, is correct?

A)Jake, because the speed of body 1 is half the speed of body 2, but m1v1 = m²v2.
B)Jane, because work does not depend on mass, only on force times distance.
C)Jake, because all bodies travel equal distances when equal forces are applied for equal times.
D)Jane, because it takes the same time for all bodies to travel equal distances when equal forces are involved.
E)Neither, because we can't compare the amounts of work done on bodies of different mass.

Question 36

Any change of the energy of a system occurs because of:

A)energy transfer across the boundaries of the system.
B)combustion of fuels within the system.
C)radioactive decay of elements within the system.
D)all of the above.
E)only (b) and (c) above.

Question 37

For a force to be a conservative force, when applied to a single test body:

A)it must have the same value at all points in space.
B)it must have the same direction at all points in space.
C)it must be parallel to a displacement in any direction.
D)equal work must be done in equal displacements.
E)no net work must be done for motion in closed paths.

Question 38

A spring with spring constant k = 800 N/m is compressed 12 cm from its equilibrium position. A spring with spring constant k = 400 N/m has the same elastic potential energy as the first spring when its extension is:

A)0.060 m.
B)0.085 m.
C)0.12 m.
D)0.17 m.
E)0.24 m.

Question 39

A 2.0-kg block is projected down a plane that makes an angle of 20 $\degree$ with the horizontal with an initial kinetic energy of 2.0 J. If the coefficient of kinetic friction between the block and plane is 0.40, how far will the block slide down the plane before coming to rest?

A)3.0 m
B)1.8 m
C)0.30 m
D)1.0 m
E)1.3 m

Question 40

As an object moves from point A to point B only two forces act on it: one force is non-conservative and does -30 J of work, the other force is conservative and does +50 J of work. Between A and B:

A)the kinetic energy of object increases, mechanical energy decreases.
B)the kinetic energy of object decreases, mechanical energy decreases.
C)the kinetic energy of object decreases, mechanical energy increases.
D)the kinetic energy of object increases, mechanical energy increases.
E)None of the above.

Question 41

A simple pendulum, 2.0 m in length, is released from rest when the support string is at an angle of 25 $\degree$ from the vertical. What is the speed of the suspended mass at the bottom of the swing?

Question 42

A rain cloud contains 2.66 * 107 kg of water vapour. How long would it take for a 2.0 kW pump to lift the same amount of water to an altitude of 2000 m?

Question 43

A conservative force on a particle moving along the x axis is given by $\overrightarrow{\mathbf{F}}=\left(3 x^{2}-2 x\right) \tilde{\mathbf{i}}$ . Which of the following is a potential that is associated with this force?

A) $(6 x-2) \tilde{\mathbf{i}}$
B) $(-6 x+2) \tilde{\mathbf{i}}$
C) $x^{3}-x^{2}+3$
D) $-x^{3}+x^{2}+3$
E)No answer given above is correct.

Question 44

A surprising demonstration involves dropping an egg from a third-floor window to land on a foam-rubber pad 2 in (5 cm) thick without breaking. If a 56-gram egg falls 12 m, and the foam pad stops the egg in 6.25 ms, by how much is the pad compressed?

Question 45

A 70-kg high jumper leaves the ground with a vertical velocity of 6.0 m/s. How high can he jump?

Question 46

A cricket wicketkeeper throws a cricket ball of mass 0.15 kg at a speed of 40 m/s and initial angle of 30 $\degree$ . What is the kinetic energy of the cricket ball at the highest point of the trajectory?