2. Consider an ideal spring. Elastic Potential Energy Hooke’s Law

3. Gravitational Potential Energy Initial Final

4. The Potential Energy Function & Equilibrium For one dimensional, conservative forces Consider the force of gravity:

5. The Potential Energy Function & Equilibrium For one dimensional, conservative forces Consider the spring:

6. The Potential Energy Function & Equilibrium What does the slope of this graph represent?

7. The Potential Energy Function & Equilibrium Stable Equilibrium – occurs when a small displacement results in a restoring force that accelerates the particle back towards the equilibrium position.

8. The Potential Energy Function & Equilibrium Unstable Equilibrium – occurs when a small displacement results in a force that accelerates the particle away from the equilibrium position. Consider the potential energy function for a skier on the top of hill between two valleys.

9. The Potential Energy Function & Equilibrium Neutral Equilibrium – occurs when a small displacement results in zero force so that the particle is again in equilibrium. Consider the potential energy function for an object on a plateau.

10. The Potential Energy Function & Equilibrium Example An object has the potential energy function as given below. 2 0 -2 -4 -6 -8 -10 3 2 1 0 -2 -3 2412108614 2412108614 a. Sketch the corresponding Force vs. Position graph.

11. The Potential Energy Function & Equilibrium Example An object has the potential energy function as given below. 2 0 -2 -4 -6 -8 -10 3 2 1 0 -2 -3 2412108614 2412108614 b. Identify all points of equilibrium. Stable Equilibrium Neutral Equilibrium

12. The Potential Energy Function & Equilibrium Example An object has the potential energy function as given below. 2 0 -2 -4 -6 -8 -10 2412108614 Total Mechanical Energy

13. The Potential Energy Function & Equilibrium Example An object has the potential energy function as given below. 2 0 -2 -4 -6 -8 -10 2412108614