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

The man exerts a constant force F can be treated as an object) in the direction in which the force is exerted. In a similar
on the crate. The direction of the way, the football players shown in Figure 7-1a will be more exhausted if the coach asks
force is parallel to the ramp. them to push the blocking sled all the way down the field rather than a short distance,
if they exert the same force on it over the longer distance. In Figure 7-1c, kinetic energy
gets transferred from one pool ball to the next as the two balls collide without friction
stevecoleimages/E+/Getty Images d F continue to increase as the football player pushes on it.
or breaking. Because of the large resistance to motion provided by friction between
the ground and the sled, the kinetic energy of the blocking sled in Figure 7-1a does not
These examples suggest how we should define the work done on an object or
a system by a force exerted on the object or system. Let us start by thinking about

an object. Suppose a constant force F is exerted on an object as it moves through a

displacement ,d and the force F is in the same direction as d. Then the work done
by the force equals the product of the magnitude of the force F and the magnitude of
As he exerts the force, the crate moves
through a displacement d up the ramp.
the displacement, d, over which the point of contact where the force is exerted on the
object moves:
Figure 7-2 Work depends on force

and displacement If the force F the
man exerts on the crate is in the same

direction as the displacement d of Work done on an object by a constant force F exerted
the point on which he is exerting the on the object in the same direction as the object's
displacement d
force on the crate, the work W that he Magnitude of the constant force F
does on the crate is the product of that
force and displacement: W = Fd. W = Fd
EQUATION IN WORDS (7-1)
Work done by a constant Magnitude of the displacement d
force exerted on an object
in the same direction as Note that Equation 7-1 refers only to situations in which the force is exerted on
the object’s displacement
the object in the same direction as the object’s displacement. You’ve already seen two
situations of this sort: The football players in Figure 7-1a push the sled backward as
it moves backward, and the man in Figure 7-2 pushes the crate uphill as it moves
uphill. Later we’ll consider the case in which force and displacement are not in the
AP ® Exam Tip same direction.
We saw in Chapters 4 and 5 that it’s important to keep track of which object
You always need to put units
on a numerical answer, but Nm exerts a given force and on which object that force is exerted. It’s equally important to
and J are both acceptable SI keep track of both the object which exerts a force and the object on which the force
units for energy. does work (and these are the same observations!). For example, in Figure 7-2, the
object exerting a force is the man, and the object on which the force is exerted and on
which work is done is the crate. Just like a force must be exerted by something exter-
nal to the object or the system, work is done on an object or a system by an external
force. Work is the first way we will explore how to transfer energy.
AP ® Exam Tip
We know that the unit of force is the newton and the unit of distance is the
There is not a symbol called meter. Therefore, the unit of work is the newton · meter, or Nm. This unit is also
weight on the AP® equation called the joule (J), named after the nineteenth-century English physicist James Joule,
sheet, but the force of gravity who did fundamental research on the relationship between motion and work. From
between two objects with Equation 7-1,
mass is given, and then is 1 J = (1N)(1m)
used in the definition of the
gravitational field. The force You do 1 J of work when you exert a 1-N push on an object in the direction it is
of gravity near the surface of moving as it moves through a distance of 1 m.
Earth is weight. While weight
is not defined on the equation
sheet, a symbol representing WATCH OUT !
weight may be defined for
you in AP® problems. Always Don’t use w as a symbol for weight.
carefully note the definition Because work and weight begin with the same letter, it’s important to use different
of all symbols introduced in a symbols to represent them in equations. We’ll use an uppercase W for work and
problem statement, and be sure g F or mg for weight (the magnitude of the gravitational force on an object near
to carefully define any symbols the surface of Earth), and we recommend that you do the same to prevent
you introduce. confusion.

Uncorrected proofs have been used in this sample. Copyright © Bedford, Freeman & Worth Publishers.
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