Deck 8: Potential Energy and Conservation of Energy

Question 1

Which one of the following five quantities CANNOT be used as a unit of potential energy?

A) watt.second
B) gram.cm/s²
C) joule
D) kg.m²/s²
E) ft.lb

Answer 1

gram.cm/s²

Question 2

A body at rest in a system is capable of doing work if:

A) the potential energy of the system is positive
B) the potential energy of the system is is negative
C) it is free to move in such a way as to decrease its kinetic energy
D) it is free to move in such a way as to decrease the potential energy of the system
E) it is free to move in such a way as to increase the potential energy of the system

Answer 2

it is free to move in such a way as to decrease the potential energy of the system

Question 3

An elevator is rising at constant speed. Consider the following statements: I. the upward cable force is constant
II. the kinetic energy of the elevator is constant
III. the gravitational potential energy of the Earth-elevator system is constant
IV. the acceleration of the elevator is zero
V. the mechanical energy of the Earth-elevator system is constant

A) all five are true
B) only II and V are true
C) only IV and V are true
D) all but III are true
E) only I, II, and IV are true

Answer 3

only I, II, and IV are true

Question 4

A good example of kinetic energy is provided by:

A) a wound-up clock spring
B) the raised weights of a grandfather's clock
C) a tornado
D) a gallon of gasoline
E) an automobile storage battery

Question 5

A 0.20-kg particle moves along the x axis under the influence of a conservative force. The potential energy is given by U(x) = (8.0 J/m²)x² + (2.0 J/m⁴)x⁴,
Where x is in coordinate of the particle. If the particle has a speed of 5.0 m/s when it is at x = 1.0 m, its speed when it is at the origin is:

A) 0 m/s
B) 2.5 m/s
C) 5.7 m/s
D) 7.9 m/s
E) 11 m/s

Question 6

A 6.0-kg block is released from rest 80 m above the ground. When it has fallen 60 m its kinetic energy is approximately:

A) 4700 J
B) 3500 J
C) 1200 J
D) 120 J
E) 60 J

Question 7

A force of 10 N holds an ideal spring with a 20-N/m spring constant in compression. The potential energy stored in the spring is:

A) 0.5 J
B) 2.5 J
C) 5 J
D) 10 J
E) 200 J

Question 8

A golf ball is struck by a golf club and falls on a green eight feet above the tee. The potential energy of the Earth-ball system is greatest:

A) just before the ball is struck
B) just after the ball is struck
C) just after the ball lands on the green
D) when the ball comes to rest on the green
E) when the ball reaches the highest point in its flight

Question 9

A 2-kg block is thrown upward from a point 20 m above the Earth's surface. At what height above Earth's surface will the gravitational potential energy of the Earth-block system have increased by 500 J?

A) 5 m
B) 25 m
C) 46 m
D) 70 m
E) 270 m

Question 10

A ball is held at a height H above a floor. It is then released and falls to the floor. If air resistance can be ignored, which of the five graphs below correctly gives the mechanical energy E of the Earth-ball system as a function of the altitude y of the ball?

A) I
B) II
C) III
D) IV
E) V

Question 11

The wound spring of a clock possesses:

A) kinetic but no potential energy
B) potential but no kinetic energy
C) both potential and kinetic energy in equal amounts
D) neither potential nor kinetic energy
E) both potential and kinetic energy, but more kinetic energy than potential energy

Question 12

Only if a force on a particle is conservative:

A) does it do no work when the particle moves exactly once around any closed path
B) does the work it does equal the change in the kinetic energy of the particle
C) does it obey Newton's second law
D) does it obey Newton's third law
E) it is not a frictional force

Question 13

Suppose that the fundamental dimensions are taken to be: force (F), velocity (V) and time (T). The dimensions of potential energy are then:

A) F/T
B) FVT
C) FV/T
D) F/T²
E) FV²/T²

Question 14

Two particles interact by conservative forces. In addition, an external force acts on each particle. They complete round trips, ending at the points where they started. Which of the following must have the same values at the beginning and end of this trip?

A) a total kinetic energy of the two-particle system
B) the potential energy of the two-particle system
C) the mechanical energy of the two-particle system
D) the total linear momentum of the two-particle system
E) none of the above

Question 15

A force on a particle is conservative if:

A) its work equals the change in the kinetic energy of the particle
B) it obeys Newton's second law
C) it obeys Newton's third law
D) its work depends on the end points of the motion, not this the path between
E) it is not a frictional force

Question 16

The sum of the kinetic and potential energies of a system of objects is conserved:

A) only when no external force acts on the objects
B) only when the objects move along closed paths
C) only when the work done by the resultant external force is zero
D) always
E) none of the above

Question 17

A 0.50-kg block attached to an ideal spring with a spring constant of 80 N/m oscillates on a horizontal frictionless surface. The total mechanical energy is 0.12 J. The greatest extension of the spring from its equilibrium length is:

A) 1.5 * 10^-3 m
B) 3.0 * 10^-3 m
C) 0.039 m
D) 0.055 m
E) 18 m

Question 18

A nonconservative force:

A) violates Newton's second law
B) violates Newton's third law
C) cannot do any work
D) must be perpendicular to the velocity of the particle on which it acts
E) none of the above

Question 19

Two objects interact with each other and with no other objects. Initially object A has a speed of 5 m/s and object B has a speed of 10 m/s. In the course of their motion they return to their initial positions. Then A has a speed of 4 m/s and B has a speed of 7 m/s. We can conclude:

A) the potential energy changed from the beginning to the end of the trip
B) mechanical energy was increased by nonconservative forces
C) mechanical energy was decreased by nonconservative forces
D) mechanical energy was increased by conservative forces
E) mechanical energy was decreased by conservative forces

Question 20

No kinetic energy is possessed by:

A) a shooting star
B) a rotating propeller on a moving airplane
C) a pendulum at the bottom of its swing
D) an elevator standing at the fifth floor
E) a cyclone

Question 21

Which of the five graphs correctly shows the potential energy of a spring as a function of its elongation x?

A) I
B) II
C) III
D) IV
E) V

Question 22

A rectangular block is moving along a frictionless path when it encounters the circular loop as shown. The block passes points 1,2,3,4,1 before returning to the horizontal track. At point 3:

A) its mechanical energy is a minimum
B) the forces on it are balanced
C) it is not accelerating
D) its speed is a minimum
E) it experiences a net upward force

Question 23

The string in the figure is 50 cm long. When the ball is released from rest, it swings along the dotted arc. How fast is it going at the lowest point in its swing?

A) 2.0 m/s
B) 2.2 m/s
C) 3.1 m/s
D) 4.4 m/s
E) 6.0 m/s

Question 24

A block of mass m is initially moving to the right on a horizontal frictionless surface at a speed v. It then compresses a spring of spring constant k. At the instant when the kinetic energy of the block is equal to the potential energy of the spring, the spring is compressed a distance of:

A)
B) (1/2)mv²
C) (1/4)mv²
D) mv²/4k
E) (1/4)

Question 25

A particle moves along the x axis under the influence of a stationary object. The net force on the particle, which is conservative, is given by F = (8N/m³)x³. If the potential energy is taken to be zero for x = 0 then the potential energy is given by:

A) (2 J/m⁴)x⁴
B) (-2 J/m⁴)x⁴
C) (24 J/m²)x²
D) (-24 J/m²)x²
E) 5 J - (2 J/m⁴)x⁴

Question 26

A toy cork gun contains a spring whose spring constant is 10.0 N/m. The spring is compressed 5.00 cm and then used to propel a 6.00-g cork. The cork, however, sticks to the spring for 1.00 cm beyond its unstretched length before separation occurs. The muzzle velocity of this cork is:

A) 1.02 m/s
B) 1.41 m/s
C) 2.00 m/s
D) 2.04 m/s
E) 4.00 m/s

Question 27

A projectile of mass 0.50 kg is fired with an initial speed of 10 m/s at an angle of 60 $\degree$ above the horizontal. The potential energy of the projectile-Earth system when the projectile is at its highest point (relative to the potential energy when the projectile is at ground level) is:

A) 25 J
B) 18.75 J
C) 12.5 J
D) 6.25 J
E) none of these

Question 28

The potential energy of a body of mass m is given by U = -mgx + 1/2kx². The corresponding force is:

A) -mgx²/2 + kx³/6
B) mgx²/2 - kx³/6
C) -mg + kx/2
D) -mg + kx
E) mg - kx

Question 29

A small object of mass m starts at rest at the position shown and slides along the frictionless loop-the-loop track of radius R. What is the smallest value of y such that the object will slide without losing contact with the track?

A) R/4
B) R/2
C) R
D) 2R
E) 0

Question 30

A 700-N man jumps out of a window into a fire net 10 m below. The net stretches 2 m before bringing the man to rest and tossing him back into the air. The maximum potential energy of the net, compared to its unstretched potential energy, is:

A) 300 J
B) 710 J
C) 850 J
D) 7000 J
E) 8400 J

Question 31

A 0.50-kg block attached to an ideal spring with a spring constant of 80 N/m oscillates on a horizontal frictionless surface. The total mechanical energy is 0.12 J. The greatest speed of the block is:

A) 0.15 m/s
B) 0.24 m/s
C) 0.49 m/s
D) 0.69 m/s
E) 1.46 m/s

Question 32

The long pendulum shown is drawn aside until the ball has risen 0.5 m. It is then given an initial speed of 3.0 m/s. The speed of the ball at its lowest position is:

A) 0 m/s
B) 0.89 m/s
C) 3.1 m/s
D) 3.7 m/s
E) 4.3 m/s

Question 33

A 0.5-kg block slides along a horizontal frictionless surface at 2 m/s. It is brought to rest by compressing a very long spring of spring constant 800 N/m. The maximum spring compression is:

A) 0.6 cm
B) 3 cm
C) 5 cm
D) 7 cm
E) 8 cm

Question 34

A small object of mass m, on the end of a light cord, is held horizontally at a distance r from a fixed support as shown. The object is then released. What is the tension in the cord when the object is at the lowest point of its swing?

A) mg/2
B) mg
C) 2 mg
D) 3 mg
E) mgr

Question 35

The graphs below show the magnitude of the force on a particle as the particle moves along the positive x axis from the origin to x = x₁. The force is parallel to the x axis and is conservative. The maximum magnitude F₁ has the same value for all graphs. Rank the situations according to the change in the potential energy associated with the force, least (or most negative) to greatest (or most positive).

A) 3, 1, 2
B) 1, 3, 2
C) 2, 3, 1
D) 3, 2, 1
E) 2, 1, 3

Question 36

A 0.50-kg block attached to an ideal spring with a spring constant of 80 N/m oscillates on a horizontal frictionless surface. When the spring is 4.0 cm longer than its equilibrium length, the speed of the block is 0.50 m/s. The greatest speed of the block is:

A) 0.32 m/s
B) 0.55 m/s
C) 0.71 m/s
D) 0.87 m/s
E) 0.93 m/s

Question 37

For a block of mass m to slide without friction up the rise of height h shown, it must have a minimum initial kinetic energy of:

A) gh
B) mgh
C) gh/2
D) mgh/2
E) 2mgh

Question 38

A simple pendulum consists of a 2.0 kg mass attached to a string. It is released from rest at X as shown. Its speed at the lowest point Y is:

A) 1.9 m/s
B) 3.7 m/s
C) 4.4 m/s
D) 6.0 m/s
E) 36 m/s

Question 39

A small object slides along the frictionless loop-the-loop with a diameter of 3 m. What minimum speed must it have at the top of the loop in order to remain in contact with the loop?

A) 1.9 m/s
B) 3.8 m/s
C) 5.4 m/s
D) 15 m/s
E) 29 m/s

Question 40

An ideal spring is used to fire a 15.0-g block horizontally. The spring has a spring constant of 20 N/m and is initially compressed by 7.0 cm. The kinetic energy of the block as it leaves the spring is:

A) 0 J
B) 2.5 *10^-2 J
C) 4.9 * 10^-2 J
D) 9.8 * 10^-2 J
E) 1.4 J

Question 41

The potential energy for the interaction between the two atoms in a diatomic molecule is U = A/x¹² - B/x⁶, where A and B are constants and x is the interatomic distance. The magnitude of the force that one atom exerts on the other is:

A) 12A/x¹³ - 6B/x⁷
B) -13A/x¹³ + 7B/x⁷
C) -11A/x¹¹ + 5B/x⁵
D) 72A/x¹² - 72B/x⁶
E) A/x¹³ - B/x⁷

Question 42

The potential energy of a particle moving along the x axis is given by U(x) = (8.0 J/m²)x² + (2.0 J/m⁴)x⁴.
If the total mechanical energy is 9.0 J, the limits of motion are:

A) -0.96 m; +0.96 m
B) -2.2 m; +2.2 m
C) -1.6 m; +1.6 m
D) -0.96 m; +2.2 m
E) -0.96 m; +1.6 m

Question 43

A block slides across a rough horizontal table top. The work done by friction changes:

A) only the kinetic energy
B) only the potential energy
C) only the thermal energy
D) only the kinetic and potential energies
E) only the kinetic and thermal energies

Question 44

The diagram shows a plot of the potential energy as a function of x for a particle moving along the x axis. The points of stable equilibrium are:

A) only a
B) only b
C) only c
D) only d
E) b and d

Question 45

The diagram shows a plot of the potential energy as a function of x for a particle moving along the x axis. The points of unstable equilibrium are:

A) only a
B) only b
C) only c
D) only d
E) b and d

Question 46

In this graph of potential energy vs. x, the horizontal line represents the total mechanical energy of a particle. Approximately what is its kinetic energy at x = 15 m?

A) 5 J
B) 10 J
C) 15 J
D) 20 J
E) 25 J

Question 47

Given a potential energy function U(x), the corresponding force is in the positive x direction if:

A) U is positive
B) U is negative
C) U is an increasing function of x
D) U is a decreasing function of x
E) it is impossible to obtain the direction of from U

Question 48

The first graph shows the potential energy U(x) for a particle moving on the x axis. Which of the following five graphs correctly gives the force F exerted on the particle?

A) I
B) II
C) III
D) IV
E) V

Question 49

Three identical blocks move either on a horizontal surface, up a plane, or down a plane, as shown below. They all start with the same speed and continue to move until brought to rest by friction. Rank the three situations according to the mechanical energy dissipated by friction, least to greatest.

A) The same for all cases
B) 1, 2, 3
C) 1, then 2 and 3 tie
D) 3, 1, 2
E) 2, 1, 3

Question 50

A 2.2-kg block starts from rest on a rough inclined plane that makes an angle of 25 $\degree$ with the horizontal. The coefficient of kinetic friction is 0.25. As the block goes 2.0 m down the plane, the mechanical energy of the Earth-block system changes by:

A) 0 J
B) -9.8 J
C) 9.8 J
D) -18 J
E) 18 J

Question 51

The diagram shows a plot of the potential energy as a function of x for a particle moving along the x axis. The points of neutral equilibrium are:

A) only a
B) only b
C) only c
D) only d
E) b and d

Question 52

The potential energy of a 0.20-kg particle moving along the x axis is given by U(x) = (8.0 J/m²)x² − (2.0 J/m⁴)x⁴. When the particle is at x = 1.0 m the magnitude of its acceleration is:

A) 0 m/s²
B) -8 m/s²
C) 8 m/s²
D) -40 m/s²
E) 40 m/s²

Question 53

A stationary mass m = 1.3 kg is hanging from a spring of spring constant k = 1200 N/m. You raise the mass a distance of 10 cm above its equilibrium position. How much has the potential energy of the mass-spring system changed?

A) 1.3 J
B) 6.0 J
C) 7.3 J
D) 12 J
E) 13 J

Question 54

Objects A and B interact with each other via both conservative and nonconservative forces. Let K_A and K_B be the kinetic energies, U be the potential energy, and E_int be the internal energy. If no external agent does work on the objects then:

A) K_A + U is conserved
B) K_A + U + E_int is conserved
C) K_A + K_B + E_int is conserved
D) K_A + K_B + U is conserved
E) K_A + K_B + U + E_int is conserved

Question 55

The potential energy of a 0.20-kg particle moving along the x axis is given by U(x) =(8.0 J/m²)x² + (2.0 J/m⁴)x^4.
When the particle is at x = 1.0 m it is traveling in the positive x direction with a speed of 5.0 m/s. It next stops momentarily to turn around at x =

A) 0 m
B) -1.1 m
C) 1.1 m
D) -2.3 m
E) 2.3 m

Question 56

A 5-kg projectile is fired over level ground with a velocity of 200 m/s at an angle of 25 $\degree$ above the horizontal. Just before it hits the ground its speed is 150 m/s. Over the entire trip the change in the thermal energy of the projectile and air is:

A) +6300 J
B) -6300 J
C) +44,000 J
D) -44,000 J
E) 0 J

Question 57

The thermal energy of a system consisting of a thrown ball, Earth, and the air is most closely associated with:

A) the gravitational interaction of the Earth and the ball
B) the kinetic energy of the ball as a whole
C) motions of the individual particles within the ball
D) motions of individual particles within the ball and the air
E) the kinetic energy of Earth as a whole

Question 58

A 25-g ball is released from rest 80 m above the surface of the Earth. During the fall the total thermal energy of the ball and air increases by15 J. Just before it hits the surface its speed is

A) 19 m/s
B) 35 m/s
C) 40 m/s
D) 45 m/s
E) 53 m/s

Question 59

A particle is released from rest at the point x = a and moves along the x axis subject to the potential energy function U(x) shown. The particle:

A) moves to a point to the left of x = e, stops and remains at rest
B) moves to the point x = e, then moves to the left
C) moves to infinity at varying speed
D) moves to x = b where it remains at rest
E) moves to x = e and then to x = d, where it remains at rest

Question 60

As a particle moves along the x axis it is acted by a conservative force. The potential energy is shown below as a function of the coordinate x of the particle. Rank the labeled regions according to the magnitude of the force, least to greatest.

A) AB, BC, CD
B) AB, CD, BC
C) BC, CD, AB
D) BC, AB, CD
E) CD, BC, AB

Question 61

The energy of a system increases at a rate of 3.5 t + 6.2 t², in joules. What is the instantaneous power at t = 3.1 s?

A) 3.5 W
B) 6.2 W
C) 16 W
D) 42 W
E) 70 W

Question 62

A stationary mass m = 1.3 kg is hanging from a spring of spring constant k = 1200 N/m. You raise the mass a distance of 10 cm above its equilibrium position in a time of 1.4 s. What was the average power expended?

A) 0.93 W
B) 4.3 W
C) 5.2 W
D) 8.6 W
E) 10.2 W

Question 63

A 0.75-kg block slides on a rough horizontal table top. Just before it hits a horizontal ideal spring its speed is 3.5 m/s. It compresses the spring 5.7 cm before coming to rest. If the spring constant is 1200 N/m, the thermal energy of the block and the table top must have:

A) not changed
B) decreased by 1.9 J
C) decreased by 2.6 J
D) increased by 1.9 J
E) increased by 2.6 J