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2. Chapter 7 Potential Energy and Conservation of Energy

3. Main Points of Chapter 7 Potential energy Conservation of energy Energy conservation in more than one dimension Nonconservative forces

4. 7-1 Potential Energy and Conservative Forces For a conservative force, work only depends on endpoints of motion There must be a function of the endpoints that represents the work

5. 7-1 Potential Energy and Conservative Forces For work done by gravity: (7-2) U 0 is an arbitrary constant Only differences in potential energy have physical significance.

6. 7-1 Potential Energy and Conservative Forces Using the force rather than the work: (7-4) (7-5) The inverse:

7. 7-1 Potential Energy and Conservative Forces Definition of total mechanical energy: (7-7) Total mechanical energy is conserved if only conservative forces are acting. Conservation of Energy

8. 7-1 Potential Energy and Conservative Forces Mass on a spring (7-12) (7-13) Spring force: Potential energy:

9. 7-2 Energy Conservation and Allowed Motion Total energy is constant As kinetic energy increases, potential energy decreases, and vice versa The maximum potential energy occurs when the kinetic energy is zero

10. 7-2 Energy Conservation and Allowed Motion Part of a cycle of a mass on a spring, showing pure potential energy, a mix, and pure kinetic energy:

11. 7-2 Energy Conservation and Allowed Motion Potential energy curves: Object cannot move farther than the point where all energy is potential

12. 7-2 Energy Conservation and Allowed Motion Equilibrium Stable equilibrium: force returns object to place where F=0 Unstable equilibrium: force moves object away from place where F=0 Neutral equilibrium: force is zero over an extended distance

13. 7-2 Energy Conservation and Allowed Motion Equilibrium

14. 7-3 Motion in Two or Three Dimensions Potential surfaces can be visualized as topographic maps Total energy depends on speed and position in 3-d space: Potential energy for projectile motion: (7-15) Same as before, as force is only in y-direction

15. 7-3 Motion in Two or Three Dimensions Central Forces (7-17) General form: Force depends only on distance r from a central point

16. 7-3 Motion in Two or Three Dimensions Central Forces Specific example: the gravitational force Potential energy: Force:

17. 7-4 Is Energy Conservation a General Principle? Yes! Need to include all types of energy – thermal, sound, light, electric, etc All fundamental forces are conservative – conservation of energy always holds One of the most fundamental principles of physics

18. Energy Conservation and Nonconservative Forces Total mechanical energy not conserved when nonconservative forces present Work done by nonconservative forces equals change in mechanical energy Total energy is conserved when all forms are counted (7-18) 7-4 Is Energy Conservation a General Principle?

19. Summary of Chapter 7 Potential energy can be defined for conservative forces Total mechanical energy conserved if all forces conservative In repetitive motion, energy changes from all kinetic to all potential and back Stable, unstable, and neutral equilibrium Energy conservation – including all forms of energy – is one of the foundations of physics