lecture 12

lecture 12 - Lecture 12 Potential energy Conservative...

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1 Lecture 12 Potential energy Conservative forces Mechanical energy Conservation of energy Appendix: Conservative forces
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2 Potential energy is energy associated with the configuration of a system of objects that exert forces on one another. Gravitational potential energy Elastic potential energy
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3 When launching a ball straight up: W < 0 on the way up (KE decreased) W > 0 on the way down (KE increased) The change in KE must go to/come from somewhere. Define the change in gravitational potential energy as g g W K U - = - = The force of gravity does work on the ball, transferring energy from K to U.
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4 Values of gravitational potential energy ( 29 ( 29 ( 29 i f y y i f y y mg dy mg U U d W U f i - = - - = - - = - = y y r F ˆ ˆ g g g U i is the potential energy at the point y i . Usually take U i = 0 at y = y i so that U(y) = mgy, where y is measured from the reference point y i .
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5 ceiling floor Example: A 2.00 kg mass hangs suspended from a string. The ceiling is 3.00 m above the floor and the length of the string is 1.00 m. (a) What is the gravitational potential energy of the mass if the ceiling is the reference point? ( 29 ( 29 ( 29 J 6 . 19 m 00 . 1 m/s 8 . 9 kg 00 . 2 2 g - = - = = mgy U
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(c) What is the gravitational potential energy of the mass if the ball’s location is the reference point? (b) What is the gravitational potential energy of the mass if the floor is the reference point? Example continued
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lecture 12 - Lecture 12 Potential energy Conservative...

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