# POTENTIAL ENERGY AND CONSERVATION OF ENERGY

1. Only if a force on a particle is conservative:
A. is its work zero when the particle moves exactly once around any closed path
B. is its work always equal to 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. is it not a frictional force
ans: A
2. 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
ans: E
3. 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
ans: E
4. 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 every motion, not on the path between
E. it is not a frictional force
ans: D
5. 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. the 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
ans: B
102 Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERGY
www.allonlinefree.com
6. 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
ans: C
7. A good example of kinetic energy is provided by:
A. a wound clock spring
B. the raised weights of a grandfather’s clock
D. a gallon of gasoline
E. an automobile storage battery
ans: C
8. 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
ans: D
9. 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
ans: B
10. 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 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
ans: D
Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERGY 103
www.allonlinefree.com
11. 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
ans: B
12. 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
ans: B
13. 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. 4800 J
B. 3500 J
C. 1200 J
D. 120 J
E. 60 J
ans: B
Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERGY 105
www.allonlinefree.com
14. A 2-kg block is thrown upward from a point 20 m above 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
ans: C
15. 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. only I, II, and III are true
E. only I, II, and IV are true
ans: E
16. A projectile of mass 0.50 kg is fired with an initial speed of 10 m/s at an angle of 60◦ above
the horizontal. The potential energy of the projectile-Earth system (relative 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
ans: B
17. 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
ans: B
18. An ideal spring is used to fire a 15.0-g pellet horizontally. The spring has a spring constant of
20 N/m and is initially compressed by 7.0 cm. The kinetic energy of the pellet as it leaves the
spring is:
A. zero
B. 2.5 × 10−2 J
C. 4.9 × 10−2 J
D. 9.8 × 10−2 J
E. 1.4 J
ans: C
19. 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. 0.054 m
E. 18 m
ans: D
20. 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
ans: D
21. 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. 0.23 m/s
B. 0.32 m/s
C. 0.55 m/s
D. 0.71 m/s
E. 0.93 m/s
ans: D
Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERGY 109
www.allonlinefree.com
22. 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
B. 3 cm
C. 5 cm
D. 80 cm
E. 80 m
ans: C
23. 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. v
0m/2k
B. (1/2)mv2
C. (1/4)mv2
D. mv2/4k
E. (1/4)0mv/k
ans: A
24. 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
ans: E
25. Objects A and B interact with each other via both conservative and nonconservative forces.
Let KA and KB be the kinetic energies, U be the potential energy, and Eint be the thermal
energy. If no external agent does work on the objects then:
A. KA + U is conserved
B. KA + U + Eint is conserved
C. KA + KB + Eint is conserved
D. KA + KB + U is conserved
E. KA + KB + U + Eint is conserved
ans: E
26. 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 internal energy
D. only the kinetic and potential energies
E. only the kinetic and internal energies
ans: E
27. A 25-g ball is released from rest 80 m above the surface of Earth. During the fall the total
internal energy of the ball and air increases by 15 J. Just before it hits the surface its speed is
A. 19 m/s
B. 36 m/s
C. 40 m/s
D. 45 m/s
E. 53 m/s
ans: A
28. A 5-kg projectile is fired over level ground with a velocity of 200 m/s at an angle of 25◦ above
the horizontal. Just before it hits the ground its speed is 150 m/s. Over the entire trip the
change in the internal energy of the projectile and air is:
A. +19, 000 J
B. −19, 000 J
C. +44, 000 J
D. −44, 000 J
E. 0
ans: C
29. 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 internal 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
ans: C