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Potential Energy

Potential Energy. Gravitational and elastic. § 7.1–7.2. Potential Energy. The energy of relative position of two objects. gravity springs electric charges chemical bonds. Potential Energy. Energy is stored doing work against a potential.

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Potential Energy

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  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 Ug = mgh

  5. Elastic Potential Energy Elastic potential energy = the work to stretch or compress a spring Uel = 1/2kx2

  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: Its gravitational potential energy increases. Its kinetic energy increases. Both A and B. 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: Its gravitational potential energy increases. Its kinetic energy increases. Both A and B. 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: • Initial gravitational potential energy Ugrav 0? • Final gravitational potential energy Ugrav f? • Change in gravitational potential energy DUgrav? • Kinetic energy just before impact Kf?

  13. Forces and potentials The (–) spatial derivative of a potential energy function is the force from that interaction. Fx= –dU/dx Fy= –dU/dy FZ= –dU/dz (This is Calculus 3 stuff) Gravity –d(mgh)/dh = –mg Elastic –d(1/2 kx2)/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. E1 = E2 K1 + Ug1 = K2 + Ug2 1/2 mv12 + mgy1 = 1/2 mv22 + mgy2

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