1. Potential Energy Gravitational and elastic § 7.1–7.2

2. Potential Energy The energy of relative position of two objects gravity springs electric charges chemical bonds

3. Potential Energy Energy is stored doing work against a potential Potential energy increases when “the potential” does negative (< 0 ) work lifting a weight stretching a spring

4. Gravitational Potential Energy Gravitational potential energy = the work to raise an object to a height U g = mgh

5. Elastic Potential Energy Elastic potential energy = the work to stretch or compress a spring U el = 1/2 kx 2

6. Hooke’s Law Potential Source: Young and Freedman, Figure 7.14.

7. Gravity Doing Negative Work Source: Young and Freedman, Figure 7.2b.

8. Work from Potential Energy When a potential does >0 work on a body: The body’s potential energy decreases The body’s kinetic energy increases

9. Poll Question When a cute furry animal moves upward in free-fall: A.Its gravitational potential energy increases. B.Its kinetic energy increases. C.Both A and B. D.Neither A nor B.

10. Gravity Doing Positive Work Source: Young and Freedman, Figure 7.2a.

11. Poll Question When a disgusting slimy thing moves downward in free-fall: A.Its gravitational potential energy increases. B.Its kinetic energy increases. C.Both A and B. D.Neither A nor B.

12. Board Work Problem A 50-g egg released from rest from the roof of a 30-m tall building falls to the ground. Its fall is observed by a student on the roof of the building, who uses coordinates with origin at the roof, and by a student on the ground, who uses coordinates with origin at the ground. What values do the two students find for: a)Initial gravitational potential energy U grav 0 ? b)Final gravitational potential energy U grav f ? c)Change in gravitational potential energy  U grav ? d)Kinetic energy just before impact K f ?

13. Forces and potentials The (–) spatial derivative of a potential energy function is the force from that interaction. F x = –dU/dx F y = –dU/dy F Z = –dU/dz ( This is Calculus 3 stuff) Gravity –d(mgh)/dh = –mg Elastic –d( 1/2 kx 2 )/dx = –kx

14. Mechanical Energy The energy available to do work Kinetic + potential = K + U

15. Conservation of Mechanical Energy If the only force doing work is gravity, mechanical energy does not change. E 1 = E 2 K 1 + U g1 = K 2 + U g2 1/2 mv 1 2 + mgy 1 = 1/2 mv 2 2 + mgy 2

16. Example Problem 7.17 A spring of negligible mass has a force constant of k = 1600 N/m. a)How far must the spring be stretched/compressed for 3.32 J of potential energy to be stored in it? b)You place the spring vertically with one end on the floor. You then drop a 1.2-kg book from a height of 0.8 m above the top of the spring. How far will the spring be compressed?

17. Example Problem 7.74 A 2-kg block is released from rest on a 53.1° incline 4.0 m from a spring with k = 120 N/m that is attached at the bottom of the slope. The coefficients of friction between the block and the slope are  s = 0.40 and  k = 0.20. a)Find the speed of the block just before it reaches the spring. b)Find the maximum compression distance of the spring. c)The package rebounds back up the slope. How close does it get to its initial position? Source: Young and Freedman, Figure 7.43.