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Chapter 8b

# Chapter 8b - Chapter 8 Potential Energy and Conservation of...

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Chapter 8 Potential Energy and Conservation of Energy (part 2)

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RECAP Conservative forces (gravity, spring force) and non-conservative forces (friction, push-pull) Potential energy U(x,y,z) Associate with conservative forces only Depends on the position (or shape) of the body It is defined with respect to a reference point Gravitational potential energy The height y is measured from a reference level y 0 =0 where U=0. U ( y ) = mgy
Gravitational Potential Energy The gravitational potential energy is a result of the interaction of two or more bodies with gravitational force. It is a non-sense to talk about potential energy of a single body! There must be an interaction. On the Earth U g of a particle- Earth system depends only on the height of the particle relative to a reference level. 1m 2m 3m Ref. level 0m Ref. level 0m -1m 1m

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Elastic Potential Energy Describes the particle-spring interaction. The work done by a spring force is: The spring force is a conservative force. We can define a potential energy function: W s = - 1 2 kx f 2 - 1 2 kx i 2 U = - W s U = 1 2 kx f 2 - 1 2 kx i 2 x i x i x f x x
Elastic potential energy (2) Elastic potential energy with respect to the relaxed position x 0 =0 x 0 =0 x x U f - U i = 1 2 kx f 2 - 1 2 kx i 2 U f = 1 2 kx f 2 U i = 1 2 kx i 2 U = 1 2 kx 2

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Quiz Question A particle is moving in the x direction from x 0 =0 to x 1 . A conservative force F with a variable x component acts on it. The maximum value of the force is the same in all cases. Rank the situations according to the change in potential energy , with most positive first .
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Chapter 8b - Chapter 8 Potential Energy and Conservation of...

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