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7-3 Newton’s second law applied to an object allows us to determine a formula for kinetic energy 299

a rubber ball might. Although we have derived this theorem for the special case of
linear motion with constant forces, it turns out to be valid even if the object follows a
curved path and the forces exerted on it vary. (We’ll justify this claim in Section 7-5.)
The net in net force is essential to this definition. Remember, the net force exerted on
an object is the sum of all of the forces exerted on the object. If there is more than one
force exerted on an object, the work done by each individual force does not tell you the
change in kinetic energy of the object. You have to add them all.

The Meaning of the Work-Energy
Theorem for an Object
What is kinetic energy, and how does the work-energy theorem for an object help us
solve physics problems? To answer these questions let’s first return to the cart from
Figure 7-6 and imagine that it starts at rest on a horizontal floor and that its interac-
tion with the floor is such that friction with the floor can be neglected. If you give the
cart a push as in Figure 7-9a, the net force on the cart equals the force that you exert
(the upward normal force on the cart cancels the downward gravitational force), so
net
the work that you do is the net work W . The cart starts at rest, so v i = 0 and so the
2
= 1 mv is zero. After you’ve finished the push, the cart
cart’s initial kinetic energy K i 2 i
2
v = v and kinetic energy K = 1 mv . So the work-energy theorem for
has final speed f f 2
an object states that
1 1
W youoncart = K f − K i = mv 2 − 0 = mv 2
2 2
In words, this special case gives us our first interpretation of kinetic energy: An object’s
kinetic energy equals the work that was done to accelerate it from rest to its present
speed.
Now suppose your friend stands in front of the moving cart and brings it to a halt
2
= 1 mv , and its final kinetic energy is
(Figure 7-9b). The cart’s initial kinetic energy is K i 2
K f = 0 (the cart ends up at rest). The net force on the cart is the force exerted by your

(a) Making the cart speed up (b) Making the cart slow down
1 The cart slides without friction 1 The cart slides without friction
and the normal force balances and the normal force balances
the gravitational force. the gravitational force.
F n F n
d d
F cart on friend
= –F friend on cart
F you on cart F friend on cart

F g F g
2 The force you exert therefore equals 2 The force your friend 3 As the cart loses
the net force on the cart. You do exerts therefore equals the kinetic energy, it
positive work on the cart, and the net force on the cart. She pushes on your
cart gains speed and kinetic energy. does negative work on the friend and does
cart, and the cart loses positive work on
speed and kinetic energy. her.
An object’s kinetic energy
equals the work that would
need to be done on the object An object’s kinetic energy equals the
to accelerate it from rest to its work it could do on another object in
current speed. coming to rest from its current speed.
Figure 7-9 The meaning of kinetic energy We can interpret kinetic energy in terms of the amount
of energy (a) that must be transferred to an object to accelerate it from rest to a given speed or (b) the
amount of energy that can be transferred by the object as it slows to a halt.

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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