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8 Application of Conservation Principles

to Energy, Work, and Power

engel.ac/Shutterstock

YOU WILL LEARN TO:
• Identify which kinds of problems are • Identify the types of energy involved
best solved with energy conservation in an interaction between objects
and the steps to follow in solving and systems.
these problems. • Describe what power is and its
• Describe how changing the relationship to work and energy.
way you identify a system • Describe the general expression for
changes the description of gravitational potential energy and
conservation of energy (but not how to relate it to the expression
the results). used near Earth’s surface.

Total energy is always conserved, but it is constant
8-1
only for a closed, isolated system

Take a pencil in your hand and toss it upward. Consider its motion after it has left your
AP ® Exam Tip hand. In this scenario, we can define the system we are examining as the Earth–pencil
2
Recall that when defining the system. As the pencil ascends, it loses speed so its kinetic energy K = 1 2 mv decreases.
gravitational potential energy at At the same time the pencil gains height so that the gravitational potential energy of
a height y, it is defined relative to the Earth–pencil system U grav = mgy increases until the pencil comes to a stop and all
where you have defined y = 0, the energy of the system is gravitational potential energy.
which is where U = 0. The AP® As the pencil falls downward, its kinetic energy increases and the gravitational
Physics 1 equation sheet instead potential energy of the system decreases as the pencil loses height. This way of thinking
∆
has U∆= mgy, which does not about the pencil’s up-and-down motion suggests that energy is converted from one
require the definition of where type (kinetic) into a different type (gravitational potential) as the pencil rises and is
the potential energy equals zero. converted back as the pencil descends.
We learned that mechanics is the branch of physics concerned with motion.
Similarly, energy related to motion is called mechanical energy. It is easy to see that
NEED TO REVIEW? kinetic energy fits this definition since it depends on speed. Even though a system can
Turn to the Glossary in the have potential energy when nothing is moving (consider when the pencil is at the top
back of the book for definitions of the flight), potential energy is also considered a type of mechanical energy because
of bolded Key Terms. all the potential energy in a system can become kinetic energy again (such as when
the pencil descends). Another way to say this is that mechanical energy of a system is
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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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