p140w07_ct_11 - Racquetball Striking a Wall Copyright:...

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Physics 140: Winter 2007 Lecture #11 February 8, 2007 Dave Winn Racquetball Striking a Wall Copyright: Loren M. Winters Mt. Etna Andrew Davidhazy
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Quick review • Objects in motion have kinetic energy: KE = ½ mv 2 • Kinetic energy is changed when forces act along the direction of motion • Work quantifies this: • The work-energy theorem describes changes in kinetic energy • To calculate the work done by a force (or forces) just add up the work in each little part of the path ds F s d F W along = = r r W Σ = Δ KE = s d F W r r
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A cart on an air track is moving at 0.5 m/s when the air is suddenly turned off. The cart comes to rest after traveling 1 m. The experiment is repeated, but now the cart is moving at 1 m/s when the air is turned off. How far does the cart travel before coming to rest? 1: 1 m 2: 2 m 3: 3 m 4: 4 m 5: 5 m W = -F f d stop = Δ KE The work done by friction removes all the KE. When we double the starting speed the required Δ KE is 4x as large. Since the F f is the same, d stop must increase by 4x…
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Work and travel in curved paths • When the direction of motion or of forces changes, total work is summed over all little elements of the path • Calculate the dot product for each piece and sum = s d F W r r mg ds θ ( ) () mgdh s d F dh ds mgds s d F = = = r r r r θ cos cos
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Work done by gravity • For gravity, the work done on any little segment is -mgdh • The total work will be: () i f y y mg dh mg mgdh s d F W = = = = r r mg ds θ mgdh s d F = r r A B This is true for any path from A to B! The total work done by gravity as an object moves is only dependent on the height of the object at the beginning and end of the motion: W grav = -mg(y f -y i ) Gravity is conservative!
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What does this mean?
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This note was uploaded on 04/04/2008 for the course PHYSICS 140 taught by Professor Evrard during the Fall '07 term at University of Michigan.

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p140w07_ct_11 - Racquetball Striking a Wall Copyright:...

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