1. CHS: M.Kelly Potential Energy and Conservation of Energy

2. CHS: M.Kelly Potential Energy Potential energy (U): energy that can be associated with the configuration (or arrangement) of system of objects that influence one another. –Gravitational potential energy, Ug –Elastic potential energy, Ue ΔU = - W

3. CHS: M.Kelly Conservative and Nonconservative Forces The system consists of two or more objects A force acts between a particle-like object (e.g. block) in the system and the rest of the system. When the system configuration changes, the force does work (W 1 ) on the object. When the configuration change is reversed, the force reverses the energy transfer, doing work (W 2 ) in the process. Conservative force: W 1 = - W 2

4. CHS: M.Kelly Path of Independence of Conservative Forces The net work done by a conservative force on a particle moving around every closed path is zero. The work done by a conservative force on a particle between two points does not depend on the path taken by the particle.

5. CHS: M.Kelly

6. Potential energy values Gravitational Potential Energy Depends only on the vertical position (or height) of the particle relative to the reference position (y=0) Choose reference configuration to be zero height (object at y i =0) Elastic Potential Energy Example: spring and block system Choose the reference configuration to be when spring is relaxed (block at x i =0)

7. CHS: M.Kelly Conservation of Mechanical Energy Mechanical Energy, E mec, of a system is the sum of potential and kinetic energy: E mec = K + U (mechanical energy) K 2 + U 2 = K 1 + U 1 (conservation of mechanical energy) –Only in an isolated system where conservative forces cause energy changes.

8. CHS: M.Kelly

9. Energy Transformation on a Roller Coaster

10. CHS: M.Kelly If the potential energy function U is known, the force at any point can be obtained by taking the derivative of the potential.

11. CHS: M.Kelly If the force is known, and is a conservative force, then the potential energy can be obtained by integrating the force.conservative forcepotential energy

12. CHS: M.Kelly Reading the potential energy curve For one-dimensional motion, the work done is a function of the F(x) and the distance, Δx  Examine turning points:  K=0 (since U = E)  Particle changes direction Look for equilibrium points:  Are they neutral,  Stable, or  Unstable.

13. CHS: M.Kelly Work done on a system by an external force. Work is energy transferred to or from a system by means of an external force acting on the system. No friction involved:  W = ΔK + ΔU  W = Δ W mech Considering friction:  F – f k = ma  Fd = Δ E mech + f k d  Δ E th = f k d (increase in thermal energy by sliding)  W = Δ E mech + Δ E th (work done on system, friction involved)

14. CHS: M.Kelly Energy Transformation for Downhill Skiing Work done on a system by an external force. K initial + U initial + W external = K final + U final

15. CHS: M.Kelly Conservation of Energy The total energy (E) of a system can change only by energy transferred to or from the system.  W = ΔE = ΔE mech + ΔE th + ΔE int. Remember: ΔE mech are changes in ΔK and ΔU Isolated system: the total energy, E, of the system can not change.  0 = ΔE mech + ΔE th + ΔE int. (isolated system)  ΔE mech-2 = ΔE mech-1 - ΔE th - ΔE int.  We can related the total energy at one instant another instant without considering the energies at intermediate times.  Examine Sample Problems 8-7, 8-8.