PotentialEnergy

# PotentialEnergy - Physics 201 Lecture 11 Conservative...

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3/4/08 Physics 201, UW-Madison 1 Physics 201: Lecture 11 Physics 201: Lecture 11 Conservative forces Potential Energy Conservation of energy http://xkcd.com/123/

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3/4/08 Physics 201, UW-Madison 2 Work done by Variable Force: (1D) Work done by Variable Force: (1D) When the force was constant, we wrote W = F Δ x area under F vs. x plot: For variable force, we find the area by integrating: dW = F(x) dx . F x W g Δ x W = F ( x ) dx x 1 x 2 F(x) x 1 x 2 dx
3/4/08 Physics 201, UW-Madison 3 Work/KE Theorem (Variable Force) Work/KE Theorem (Variable Force) W = Fdx x 1 x 2 F = ma = m dv dt = m 1 2 (v 2 2 v 1 2 ) = 1 2 mv 2 2 1 2 mv 1 2 = Δ KE = m dv dt dx x 1 x 2 = m v dv v 1 v 2 = m v dv dx dx v 1 v 2 dv dt = dx dt dv dx = v dv dx chain rule

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3/4/08 Physics 201, UW-Madison 4 Work/Kinetic Energy Theorem: Work/Kinetic Energy Theorem: { Net Net Work Work done on object} = { change change in kinetic energy kinetic energy of object} W F = Δ K = 1 / 2 mv 2 2 - 1 / 2 mv 1 2 Δ x F v 1 v 2 m W F = F Δ x
3/4/08 Physics 201, UW-Madison 5 Power Power You recognize that there is a difference in running up the stairs and walking up the stairs. P = Δ E Δ t = dE dt Units of power: J/sec = N-m/sec = Watts 1 hp = 746 W Or…the rate at which energy is transformed is also power. P = dW dt Power is the “rate of doing work”: If the force does not depend on time: P = dW dt = d dt r F net i d r r ( ) = r F net i d r r dt = r F net i r v

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3/4/08 Physics 201, UW-Madison 6 Work done by gravity:
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## This note was uploaded on 03/27/2008 for the course PHYS 201 taught by Professor Walker during the Spring '08 term at University of Wisconsin.

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PotentialEnergy - Physics 201 Lecture 11 Conservative...

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