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7-4 The work-energy theorem can simplify many physics problems 303

7-4 The work-energy theorem can simplify
many physics problems

In this section we’ll explore the relationships among work, force, and speed by apply-
ing the definitions of work and kinetic energy (Equations 7-2 and 7-8) and the work-
energy theorem for an object (Equation 7-9) to a variety of physical situations. Even
if the problem could be solved using Newton’s second law, the work-energy theorem
often makes the solution easier as well as gives additional insight.
Shortly, we will find out there are many more ways to use the work-energy theorem
for an object, but we will start with the simplest case: problems that involve an object
that moves a distance along a line while constant forces are being exerted on it. You
can use this theorem to relate the forces exerted on the object, the displacement of the
object, and the speed of the object at the beginning and end of the displacement.
Note that the work-energy theorem for an object makes no reference to the time it
takes the object to move through this displacement. If the problem requires you to use
or find this time, you should use a different approach, such as using Newton’s laws in
conjunction with kinematics.
Just as we described in Example 1-1, a strategy for solving problems involves three
steps, which below we tie directly to problems using the work-energy theorem for an
object:

Set Up
Always draw a picture of the situation that shows the object’s displacement. Include a AP ® Exam Tip
free-body diagram, showing all the forces exerted on the object. Draw the direction of Practice drawing free-body
each force carefully, because the direction is crucial for determining how much work diagrams and sketches of
each force exerted on the object does on the object. Decide what unknown quantity the setups; they are often required
problem is asking you to determine (for example, the object’s final speed or the magni- on the AP® Physics exam.
tude of one of the forces).

Solve
Use Equation 7-2 to find expressions for the work done by each force exerted on the
object. It can be helpful to create secondary diagrams on which you place the vector
representing the force tail-to-tail with the vector representing displacement to deter-
mine the angle between them. This can be repeated for each force for which you want
to calculate the work done. The sum of the work done by each force is the net work
done on the object, W . Then use Equations 7-8 and 7-9 to relate this to the object’s
net
initial and final kinetic energies. Solve the resulting equations for the desired unknown.
Reflect
Always check whether the numbers have reasonable values and that each quantity has
the correct units.

EXAMPLE 7-4 Work and Kinetic Energy: Force at an Angle
At the start of a race, a four-man bobsleigh crew pushes their sleigh as fast as they
can down the 50.0-m straight, relatively horizontal starting stretch (Figure 7-10). The
force that the four men together exert on the 210-kg sleigh has magnitude 285 N
and is directed at an angle of 20.0 ° below the horizontal. As they push, a 60.0-N net
kinetic friction and air drag force is also exerted on the sleigh. What is the speed of the
sleigh right before the crew jumps in at the end of the starting stretch? sampics/Corbis/Getty Images

Figure 7-10 Bobsleigh start The success of a bobsleigh team depends on the team members
giving the sleigh a competitive starting 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.

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