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306 Chapter 7 Conservation of Energy and an Introduction to Energy and Work

THE TAKEAWAY for Section 7-4

✔ The work-energy theorem for an object allows us to that are exerted on the object in question, and indicates the
explore the relationship between the force exerted on an object, object’s displacement. Then write expressions for the kinetic
the displacement through which the object travels, and its speed energies at the beginning and end of the displacement and for
in a variety of physical situations. the net work done on the object (the sum of the work done by

✔ To solve problems using the work-energy theorem for an each force). Relate these using the work-energy theorem for an
object, begin by drawing a diagram that shows all the forces object and solve for the unknown quantity.
Prep for the AP ® Exam

Building Blocks object as alternative scientific explanations in terms of
the role of time.
1. Two model racing cars are propelled by identical launchers. EX 4. In a baseball game, assume the ball is thrown from the
One car has twice the mass of the other. Qualitatively 7-5 pitcher to the catcher at a constant velocity, v . We can
describe the relative maximum speeds of the two cars. make this assumption, that the ball travels in a horizontal
EX 2. Calculate the final speed of a 2.00-kg object that is line from the pitcher to the catcher, if we neglect gravity,
7-4 pushed for 22.0 m by a 40.0-N force directed 20.0° below which over the time of flight is reasonable, given the

the horizontal on a smooth, level floor. Assume the object speed delivered by a professional pitcher. After contacting
starts from rest. the glove, the ball travels only a small distance, d , before
at rest v = ? coming to a complete stop.
2.00 kg 2.00 kg (a) If the mass of the ball is m construct a symbolic
,

20° representation of the average horizontal force that the
40.0 N
40.0
22.0 m glove exerts on the ball during the catch in terms of v ,
,
d and m using the work-energy theorem for an object.
,

Skill Builders (b) Calculate the value of the average force for the glove on

the ball found in part (a) using v = 50 m/s, d = 10 cm ,
EX 3. A 325-g model boat is facing east and is floating on a and m = 0.145 kg.
7-4 pond. Because it is floating there is no net force exerted (c) The catcher remains in position crouching behind the

on the boat perpendicular to the water’s surface. How- batter. The catcher’s mitt is held vertically and the ball
ever, there are forces exerted on the boat in the plane of is caught in a padded pocket in the mitt. Explain why
the water’s surface. The wind in its sail provides a force of the baseball gloves used by other players have much
1.85 N that points 25.0° north of east. The average force less padding than the catcher’s mitt.

on its keel (a part of the boat’s hull that lies beneath the
water and helps prevent the boat from slipping sideways) Skills in Action
is 0.782 N pointing south. The average drag force of the
water on the boat is 0.750 N toward the west. 5. A 65.0-kg woman steps off a 10.0-m diving platform and

(a) Construct a free-body diagram of the forces exerted drops straight down into the water. After entering the

on the model boat in the plane of the water’s surface. water she continues falling through the water until she

(b) The boat starts from rest and heads east. Using the reaches a depth of 4.00 m.
work-energy theorem for an object, predict the speed (a) Calculate the work done on the woman by gravity

of the boat after it has moved through a displacement and by the water. Ignore air resistance.

of 3.55 m. (b) What is the average net force exerted on her over the

(c) Using the same initial velocity and forces, use Newton’s 4.00-m displacement in the water?

second law to predict the speed of the boat as a func- (c) How does the average net force exerted on the
tion of time. woman while she is moving downward in the water

(d) Compare your results from parts (b) and (c). Evalu- compare to the force exerted on her just by the water
ate the second law and work-energy theorem for an during this displacement?
The work-energy theorem is also valid for curved paths
7-5 and varying forces, and, with a little more information,
systems as well as objects
We’ve derived the work-energy theorem only for the special case of an object in linear
motion with constant forces. Because we already know how to solve problems for that
kind of motion, you may wonder what good this theorem is. Here’s the answer: The
work-energy theorem also works for motion along a curved path and in cases where

Uncorrected proofs have been used in this sample. Copyright © Bedford, Freeman & Worth Publishers.
Distributed by Bedford, Freeman & Worth Publishers. For review purposes only. Not for redistribution.

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