PHY221 Ch8: Conservative forces and PE

1. Recall main points: • Understand why we can define potential energy when

work is independent of path (conservative forces)• Know the definition of U and why it is defined only up

to an arbitrary constant C• Know how to define the u’s for weight, spring force,

gravity.• Be capable of proving the fact that when only

conservative forces are present, the total energy of a system is conserved

2. Discussion and examples• Know how to use conservation of energy to solve the

roller coaster problem, the freefall problem and the block on incline problem (with Wnormal force =0)

PHY221 Ch8: Conservative forces and PE1.

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Conservative Forces and Potential Energy Definitions

If W of a force is independent of path followed by mass between two points, then W can at most depend on the location of these points. Therefore W can at most be a function of the position. We call that function U, potential energy and call forces whose wok is independent of path, conservative forces. We have:

1 2 1 2( ) ( )W U p U p

PHY221 Ch8: Conservative forces and PE1.

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Mechanical Energy and Energy Conservation

This implies that: 1 1 2 2( ) ( )U P K U P K

The quantity U+K is called the total (or mechanical) energy of the system, and we just proved that this quantity is conserved ie constant during the motion, if all forces applied are conservative (or do not work, like the normal force)

PHY221 Ch8: Conservative forces and PE1.

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Example of Computation of PE:PE for weight:

PE for Gravity:

PE for a Spring force:

PHY221 Ch8: Conservative forces and PE2.

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Problem: The Roller Coaster

PHY221 Ch8: Conservative forces and PE2.

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Problem: Block on Incline and Spring (without friction)