Chapter: Chapter 7
Learning Objectives
LO 7.1.0 Solve problems related to kinetic energy
LO 7.1.1 Apply the relationship between a particle’s kinetic energy, mass, and speed.
LO 7.1.2 Identify that kinetic energy is a scalar quantity.
LO 7.2.0 Solve problems related to work and kinetic energy
LO 7.2.1 Apply the relationship between a force (magnitude and direction) and the work done on
a particle by the force when the particle undergoes a displacement.
LO 7.2.2 Calculate work by taking a dot product of the force vector and the displacement vector,
in either magnitude-angle or unit-vector notations.
LO 7.2.3 If multiple forces act on a particle, calculate the net work done by them.
LO 7.2.4 Apply the work–kinetic energy theorem to relate the work done by a force and the
resulting change in kinetic energy.
LO 7.3.0 Solve problems related to work done by the gravitational force
LO 7.3.1 Calculate the work done by the gravitational force when an object is lifted or lowered.
LO 7.3.2 Apply the work–kinetic energy theorem to situations where an object is lifted or
lowered.
LO 7.4.0 Solve problems related to work done by a spring force
LO 7.4.1 Apply the relationship (Hooke’s law) between the force on an object by a spring, the
stretch or compression of the spring, and the spring constant of the spring.
LO 7.4.2 Identify that a spring force is a variable force.
LO 7.4.3 Calculate the work done on an object by a spring force by integrating the force from the
initial position to the final position of the object or by using the known generic result of that
integration.
LO 7.4.4 Calculate the work by graphically integrating on a graph of force versus position of the
object.
LO 7.4.5 Apply the work–kinetic energy theorem to situations in which an object is moved by a
spring force.
LO 7.5.0 Solve problems related to work done by a general variable force
LO 7.5.1 Given a variable force as a function of position, calculate the work done by it on an
object by integrating the function from the initial to the final position of the object, in one or
more dimensions.
LO 7.5.2 Given a graph of force versus position, calculate the work done by graphically
integrating from the initial to the final position of the object.
LO 7.5.3 Convert a graph of acceleration versus position to a graph of force versus position.
LO 7.5.4 Apply the work–kinetic energy theorem to situations where an object is moved by a
variable force.
LO 7.6.0 Solve problems related to power
LO 7.6.1 Apply the relationship between average power, the work done by a force, and the time
interval in which that work is done.
LO 7.6.2 Given the work as a function of time, find the instantaneous power.
LO 7.6.3 Determine the instantaneous power by taking the dot product of the force vector and an
object’s velocity vector, in magnitude-angle and unit-vector notations.
Multiple Choice
1. Which of the following bodies has the largest kinetic energy?
A) Mass 3M and speed V
B) Mass 3M and speed 2V
C) Mass 2M and speed 3V
D) Mass M and speed 4V
E) All four of the above have the same kinetic energy
2. Two trailers, X with mass 500 kg and Y with mass 2000 kg, are being pulled at the same
speed. The ratio of the kinetic energy of Y to that of X is:
A) 1:1
B) 2:1
C) 4:1
D) 9:1
E) 1500:1
3. An 8000-N car is traveling at 12 m/s along a horizontal road when the brakes are applied.
The car skids to a stop in 4.0 s. How much kinetic energy does the car lose in this time?
A) 4.8 104 J
B) 5.9 104 J
C) 1.2 105 J
D) 5.8 105 J
E) 4.8 106 J
4. An object is constrained by a cord to move in a circular path of radius 0.5m on a horizontal
frictionless surface. The cord will break if its tension exceeds 16N. The maximum kinetic
energy the object can have is:
A) 4 J
B) 8 J
C) 16 J
D) 32 J
E) 64 J
5. The weight of an object on the moon is one-sixth of its weight on the Earth. The ratio of the
kinetic energy of a body on the Earth moving with speed V to that of the same body moving with
speed V on the moon is:
A) 6:1
B) 36:1
C) 1:1
D) 1:6
E) 1:36
6. Which of the following is the correct combination of dimensions for energy?
A) MLT
B) LT2 /M
C) ML2/T2
D) M2L3T
E) ML/T2
7. Which of the following is NOT a correct unit for work?
A) erg
B) ftlb
C) watt
D) newtonmeter
E) joule
8. Which of the following groups does NOT contain a scalar quantity?
A) velocity, force, energy
B) displacement, acceleration, force
C) acceleration, speed, energy
D) energy, force, distance
E) energy, weight, time
9. A boy holds a 40-N weight at arm’s length for 10 s. His arm is 1.5 m above the ground. The
work done by the force of the boy on the weight while he is holding it is:
A) 0 J
B) 6.1 J
C) 40 J
D) 60 J
E) 90 J
10. A crate moves 10 m to the right on a horizontal surface as a woman pulls on it with a 10–N
force. Rank the situations shown below according to the work done by her force, least to
greatest.
A) 1,2,3
B) 2,1,3
C) 2,3,1
D) 1,3,2
E) 3,2,1,
11. A 2-kg object is moving at 3 m/s. A 4-N force is applied in the direction of motion and then
removed after the object has traveled an additional 5 m. The work done by this force is:
A) 9 J
B) 18 J
C) 20 J
D) 29 J
E) 38 J
12. A sledge (including load) weighs 5000 N. It is pulled on level snow by a dog team exerting
a horizontal force on it. The coefficient of kinetic friction between sledge and snow is 0.05. How
much work is done by the dog team pulling the sledge 1000 m at constant speed?
A) 0 J
B) 2.5 105 J
C) 5.0 105 J
D) 2.5 106 J
E) 5.0 106 J
13. Camping equipment weighing 6000 N is pulled across a frozen lake by means of a
horizontal rope. The coefficient of kinetic friction is 0.05. The work done by the campers in
pulling the equipment 1000 m at constant velocity is:
A) 0 J
B) 1.5 105 J
C) 3.0 105 J
D) 2.9 106 J
E) 6.0 106 J
14. Camping equipment weighing 6000 N is pulled across a frozen lake by means of a
horizontal rope. The coefficient of kinetic friction is 0.05. How much work is done by the
campers in pulling the equipment 1000 m if its speed is increasing at the constant rate of 0.20
m/s2?
A) –1.2 106 J
B) 1.2 105 J
C) 3.0 105 J
D) 4.2 105 J
E) 4.1 106 J
15. A 0.50-kg object moves in a horizontal circular track with a radius of 2.5 m. An external
force of 3.0 N, always tangent to the track, causes the object to speed up as it goes around. The
work done by the external force as the mass makes one revolution is:
A) 7.5 J
B) 24 J
C) 47 J
D) 94 J
E) 120 J
16. A crate is initially at rest on a horizontal frictionless table. A constant horizontal force F is
applied. Which of the following five graphs is a correct plot of work W as a function of crate
speed v?
A) I
B) II
C) III
D) IV
E) V
17. An object moves in a circle at constant speed. The work done by the centripetal force is
zero because:
A) the displacement for each revolution is zero
B) the average force for each revolution is zero
C) there is no friction
D) the magnitude of the acceleration is zero
E) the centripetal force is perpendicular to the velocity
18. An object of mass 1 kg is whirled in a horizontal circle of radius 0.5 m at a constant speed
of 2 m/s. The work done on the object during one revolution is:
A) 0 J
B) 1 J
C) 2 J
D) 4 J
E) 16 J
19. A particle moves 5 m in the positive x direction while being acted upon by a constant force
𝐹
⃗ = (4 N)𝑖̂ + (2 N 𝑗̂) – (4 N) 𝑘
̂. The work done on the particle by this force is:
A) 20 J
B) 10 J
C) –20 J
D) 30 J
E) is impossible to calculate without knowing other forces
20. A man pulls a sled along a rough horizontal surface by applying a constant force 𝐹
⃗ at an
angle
above the horizontal. In pulling the sled a horizontal distance d, the work done by the
man is:
A) Fd
B) Fd cos
C) Fd sin
D) Fd/cos
E) Fd/sin
21. A 100-kg piano rolls down a 20° incline. A man tries to keep it from accelerating, and
manages to keep its acceleration to 1.2 m/s2. If the piano rolls 5 m, what is the net work done on
it by all the forces acting on it?
A) 60 J
B) 100 J
C) 600 J
D) 1000 J
E) 4900 J
22. An 8-N block slides down an incline. It has an initial speed of 7 m/s. The work done by the
resultant force on this block is:
A) 20 J
B) 28 J
C) 56 J
D) impossible to calculate without more information
E) none of these
23. The mechanical advantage of any machine is:
A) the efficiency of the machine
B) the work done by the machine
C) the ratio of the work done by the machine to the work expended on it
D) the ratio of the force exerted by the machine to the force applied to it
E) the ratio of the force applied to the machine to the force exerted by it
24. In raising an object to a given height by means of an inclined plane, as compared with
raising the object vertically, there is a reduction in:
A) work required
B) distance pushed
C) friction
D) force required
E) value of the acceleration due to gravity
25. Two objects with masses, m1 and m2, have the same kinetic energy and are both moving to
the right. The same constant force 𝐹
⃗ is applied to the left to both masses. If m1 = 4m2, the ratio
of the stopping distance of m1 to that of m2 is:
A) 1:4
B) 4:1
C) 1:2
D) 2:1
E) 1:1
26. At time t = 0 a particle starts moving along the x axis. If its kinetic energy increases
uniformly with t the net force acting on it must be:
A) constant
B) proportional to t
C) inversely proportional to t
D) proportional to √𝑡
E) proportional to 1/√𝑡
27. At time t = 0 a 2-kg particle has a velocity of (4 m/s) 𝑖̂ – (3 m/s) 𝑗̂. At t = 3 s its velocity is
(2 m/s) 𝑖̂ + (3 m/s) 𝑗̂. During this time the work done on it was:
A) 4 J
B) –4 J
C) –12 J
D) –40 J
E) (4 J) 𝑖̂ + (36 J) 𝑗̂
28. A particle starts from rest at time t = 0 and moves along the x axis. If the net force on it is
proportional to t, its kinetic energy is proportional to:
A) t
B) t2
C) t4
D) 1/t2
E) none of the above
29. The velocity of a particle moving along the x axis changes from vi to vf. For which values
of vi and vf is the total work done on the particle positive?
A) vi = 5m/s, vf = 2m/s
B) vi = 5m/s, vf = –2m/s
C) vi = –5m/s, vf = –2m/s
D) vi = –5m/s, vf = 2m/s
E) vi = –2m/s, vf = –5m/s
30. The amount of work required to stop a moving object is equal to the:
A) velocity of the object
B) kinetic energy of the object
C) mass of the object times its acceleration
D) mass of the object times its velocity
E) square of the velocity of the object
31. A 5.0-kg cart is moving horizontally at 6.0 m/s. In order to change its speed to 10.0 m/s, the
net work done on the cart must be:
A) 20 J
B) 40 J
C) 90 J
D) 160 J
E) 400 J
32. A 4-kg cart starts up an incline with a speed of 3 m/s and comes to rest 2 m up the incline.
The total work done on the cart is:
A) –6 J
B) –8 J
C) –12 J
D) –18 J
E) impossible to calculate without more information
33. A Boston Red Sox baseball player catches a ball of mass m that is moving toward him with
speed v. While bringing the ball to rest, his hand moves back a distance d. Assuming constant
deceleration, the horizontal force exerted on the ball by his hand is:
A) mv/d
B) mvd
C) mv2/d
D) 2mv/d
E) mv2/(2d)
34. A 0.50-kg object moves in a horizontal circular track with a radius of 2.5 m. An external
force of 3.0 N, always tangent to the track, causes the object to speed up as it goes around. If it
starts from rest its speed at the end of one revolution is:
A) 5.5 m/s
B) 14 m/s
C) 15 m/s
D) 18 m/s
E) 21 m/s
35. A 0.50-kg object moves on a horizontal frictionless circular track with a radius of 2.5 m.
An external force of 3.0 N, always tangent to the track, causes the object to speed up as it goes
around. If it starts from rest, then at the end of one revolution the radial component of the force
of the track on it is:
A) 19 N
B) 38 N
C) 47 N
D) 75 N
E) 96 N
36. An 80-N crate slides with constant speed a distance of 5.0 m downward along a rough
slope that makes an angle of 30 with the horizontal. The work done by the force of gravity is:
A) –400 J
B) –200 J
C) –69 J
D) 200 J
E) 400 J
37. A 1-kg block is lifted vertically 1 m at constant speed by a boy. The work done by the boy
is about:
A) 1 ft lb
B) 1 J
C) 10 J
D) 0.1 J
E) 0 J
38. The work done by gravity during the descent of a projectile is:
A) positive
B) negative
C) zero
D) depends for its sign on the direction of the y axis
E) depends for its sign on the direction of both the x and y axes
39. A man pulls a 100-N crate up a frictionless 30 slope 5 m high as shown. Assuming that
the crate moves at constant speed, the work done by the man is:
A) –500 J
B) –250 J