Page 18 - 2023-bfw-physics-stewart-3e-new.indd

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

WATCH OUT ! friend, so the work she does on the cart equals the net work on the cart. If we apply the
work-energy theorem for an object to the part of the motion where she exerts a force
Kinetic energy is a scalar. on the cart,
Although you have become 1 1
comfortable breaking W = K − K i = 0 − mv 2 =− mv 2
an object’s motion into friend on cart f 2 2
components, remember that
kinetic energy depends on Our discussion in Section 7-2 tells us that the cart does an amount of work on your
speed, not velocity. Because friend that’s just the negative of the work that your friend does on the cart. So we
speed is not a vector, kinetic can write
energy is a scalar quantity
and not a vector. It wouldn’t 1 2
be meaningful to set up W cart on friend =−W friend on cart = 2 mv
components of kinetic energy
in different directions. Note This gives us a second interpretation of kinetic energy: An object’s kinetic energy equals
also that we’ve only discussed the amount of work it can do in the process of coming to a halt from its present speed.
the kinetic energy associated Your friend is interacting with the floor through friction, and her hands can move a
with the motion of an object different distance than her center of mass so she cannot be modeled as an object so she
where every point must have does not end up with this kinetic energy!
exactly the same speed, in This should remind you of the general description of energy as the ability to do
the same direction, which work, which we introduced in Section 7-1.
we call translational kinetic
energy. Kinetic energy is also You already have a good understanding of this interpretation of kinetic energy.
associated with the rotation of If you see a thrown basketball coming toward your head, you know intuitively that
1
2
a system around its own axis due to its mass and speed it has a pretty good amount of kinetic energy K = 2 mv ,
where different points in the so it can do a pretty good amount of work on you (it can exert a force on your nose
system have different speeds that pushes it inward a painful distance). You don’t want this to happen, which is
and directions. We’ll return to why you duck!
this rotational kinetic energy
in later in the text.
Net Work and Net Force
In Equation 7-9 we interpret W as the work done by the net force exerted on an
net
object. But we saw in Example 7-2 that the work done by the net force equals the sum
AP ® Exam Tip of the amount of work done by each individual force exerted on the object. So we can
also think of W in Equation 7-9 as the net work done by all of the individual forces.
net
The table of equations given It turns out that this statement is true not just for the situation in Example 7-2; it
with the exam does not applies to all situations.
differentiate between the total This gives us a simplified statement of the work-energy theorem for an object:
work and the work done by a The net work done by all forces exerted on an object, W , equals the change in its
single force. It is important to kinetic energy K − net −
i K . If the net work done is positive, then K
i K is positive, the final
f
f
understand in which situations kinetic energy is greater than the initial kinetic energy, and the object gains speed. If
you would use either one, and
that just the total work—or work the net work done is negative, then K f − i K is negative, the final kinetic energy is less
done by the net force—is equal than the initial kinetic energy, and the object loses speed. If zero net work is done, the
to the change in kinetic energy kinetic energy does not change, and the object maintains the same speed (Table 7-2).
of an object. This agrees with the observations we made in Section 7-1.
Example 7-3 shows how to use the work-energy theorem for an object.

TABLE 7-2 The Work-Energy Theorem for an Object
If the net work done on …then the change in the object’s …and the speed of the
an object is… kinetic energy is K f −− K i … object…
W net > 0 (positive K f − K i > 0 (kinetic energy increases (object
net work) increases) speeds up)
W net < 0 (negative K f − K i < 0 (kinetic energy decreases (object slows
net work) decreases) down)
W net = 0 (zero net K f − K i = 0 (kinetic energy is unchanged (object
work) stays the same) maintains the same
speed)

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.

08_stewart3e_33228_ch07_284_333_8pp.indd 300 20/08/22 8:44 AM