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7-2 The work done by a constant force exerted on a moving object 293

• If the angle θ in Equation 7-2 is greater than 90 , the value of cos θ is negative.
°

In this case the work done by force F on the object is negative: W < 0. As an A lazy dog exerts a downward
force on the screen.
example, Figure 7-6 shows a cart rolling along the floor as a person tries to slow

it down. The force F that the person exerts on the cart is directed opposite

to the cart’s displacement d, so the angle θ in Equation 7-2 is 180°. Because
cos 180°= − 1, this means that the work that the person does on the cart is
W persononcart =−Fd , which is negative. F q = 90° d
What does it mean to do negative work on an object? Remember that when the force
exerted on an object (and hence the object’s acceleration) points in the opposite direction
of the object’s velocity and displacement, the object slows down (see Figure 2-9). So doing The angle between the force and
negative work on an object slows it down. Conversely, if you do positive work on an the displacement d of the screen is
90° (the force and displacement are
object, you can speed it up. This makes sense: Because work is a way to transfer energy, perpendicular). Hence the force has
if you make a positive energy transfer, you increase the energy of the system receiving zero component in the direction of
it. If you make a negative energy transfer, you decrease the system’s energy. d and does zero work.
What else happens when you do negative work on an object? Newton’s third law
provides the answer when two objects in contact exert forces on each other: If the Figure 7-5 Doing zero work A dog

person in Figure 7-6 exerts a force F on the cart, the cart exerts a force −F on her resting atop the screen exerts a force
(the same magnitude of force but in the opposite direction). The hands of the person on the screen as it slides but does zero

work on the screen.
have the same displacement d as the cart, and the force the cart exerts on her hands is
in the same direction as her hands’ displacement (θ = 0 and cos θ =+1 in Equation 7-2),
so the work that the cart does on the person is W cart on person =+Fd. For objects in con- WATCH OUT !
tact, if object A does negative work on object B, then object B does an equal amount of
positive work on object A. For example, as in Figure 7-1c, when a moving cue ball hits Not all objects exert contact
a stationary pool ball on a pool table, the cue ball does positive work on the pool ball: forces on each other!
It pushes the pool ball forward (in the direction that the pool ball moves) and makes
the pool ball speed up. The pool ball does negative work on the cue ball: It pushes While Newton’s third law
back on the cue ball (in the direction opposite to the cue ball’s motion) and makes the is always true, when objects
cue ball slow down. With the pool balls, the energy transfer is almost all kinetic. They interact by forces that do not
are modeled very well as objects. For the person pushing the box, her hands actually require contact, sometimes the
don’t necessarily move the same distance as the rest of her body, and her muscles warm objects do not move through
up, so the object model would not be the right model for the person. In this case, her the same displacement. That
is why action-reaction pair
kinetic energy doesn’t change much because of internal motion but primarily because forces do not always do equal
she is also pushing against the floor so (more Newton’s third law) the floor is pushing but opposite work.
against her, helping her stay put.

1 As the person tries to make the cart slow down, the cart and the person’s
hands move together to the right (they have the same displacement since
her hands and the cart are in contact).

d
F person on cart
F cart on person = –F person on cart

For objects in contact, if
one object (such as the
person) does negative
work on a second object
(such as the cart), the second
object does an equal amount of
positive work on the rst object.

2 The force of the person on the cart is 3 By Newton’s third law, the cart exerts an equally
opposite to the cart’s displacement. strong force on the person, but in the opposite
Hence q = 180°, cos q = –1, and the direction—that is, in the same direction of the
person does negative work on the cart. displacement of the person’s hands. So the cart
does positive work on the person.

Figure 7-6 Doing negative work As the cart rolls to the right, the person pushes on the cart to
the left in order to make it slow down. As a result, she does negative work on the cart.

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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