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Chapter 8
Conservation of Energy

Copyright © 2009 Pearson Education, Inc.

Units of Chapter 8
• Conservative and Nonconservative Forces
• Potential Energy
• Mechanical Energy and Its Conservation
• Problem Solving Using Conservation of
Mechanical Energy
• The Law of Conservation of Energy
• Energy Conservation with Dissipative Forces:
Solving Problems

Copyright © 2009 Pearson Education, Inc.

Units of Chapter 8
• Gravitational Potential Energy and Escape
Velocity
• Power
• Potential Energy Diagrams; Stable and
Unstable Equilibrium

Copyright © 2009 Pearson Education, Inc.

8-1 Conservative and Nonconservative
Forces
A force is conservative if: the work done by the force on an object moving from one point to another depends only on the initial and final positions of the object, and is independent of the particular path taken.
Example: gravity.

Copyright © 2009 Pearson Education, Inc.

8-1 Conservative and Nonconservative
Forces
Another definition of a conservative force: a force is conservative if the net work done by the force on an object moving around any closed path is zero.

Copyright © 2009 Pearson Education, Inc.

8-1 Conservative and Nonconservative
Forces
If friction is present, the work done depends not only on the starting and ending points, but also on the path taken. Friction is called a nonconservative force.

Copyright © 2009 Pearson Education, Inc.

8-1 Conservative and Nonconservative
Forces
Potential energy can only be defined for conservative forces.

Copyright © 2009 Pearson Education, Inc.

8-2 Potential Energy

An object can have potential energy by virtue of its surroundings.
Familiar examples of potential energy:
• A wound-up spring
• A stretched elastic band
• An object at some height above the ground

Copyright © 2009 Pearson Education, Inc.

8-2 Potential Energy
In raising a mass m to a height h, the work done by the external force is

.
We therefore