PHY205 Ch8: Conservative forces and PE

1. PHY205 Ch8: Conservative forces and PE • 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 • 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)

2. PHY205 Ch8: Conservative forces and PE Main Points 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:

3. PHY205 Ch8: Conservative forces and PE Main Points Mechanical Energy and Energy Conservation This implies that: The quantity U+K is called the total (or mechanical) energy of the system, E=U+K 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). In case some forces are not conservative, their work W cannot be written in terms of a potential energy U and we must write: Which we can rewrite as:

4. PHY205 Ch8: Conservative forces and PE Main Points Example of Computation of PE: PE for weight: Compute work from y1 to y2: PE for a Spring force: Compute work from equilibrium at x=0 to x PE for Gravity:

5. PHY205 Ch8: Conservative forces and PE Discuss Problem: The Roller Coaster

6. PHY205 Ch8: Conservative forces and PE Discuss Problem: Block on Incline and Spring (without friction)