lecture15

# lecture15 - Gravitational potential energy Conservation of...

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Gravitational potential energy. Conservation of energy h 1 2 ) ( 2 2 1 2 1 2 1 2 2 1 2 2 U U K K ) h mg(h mgh U W mv mv W U Definition: mgh U g ) ( 1 2 h h mg mgh W mg F g g const E U K U K 2 2 1 1 0 E U K For closed isolated system Conservation of mechanical energy:

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Example: A box of unknown mass and initial speed v 0 = 10 m/s moves up a frictionless incline. How high does the box go before it begins sliding down? m mgh mv 0 0 2 0 2 1 2 2 1 1 U K U K   m s m s m g v h 5 / 10 2 / 10 2 2 2 2 0 Only gravity does work (the normal is perpendicular to the motion), so mechanical energy is conserved. We can apply the same thing to any “incline”! h Turn-around point: where K = 0 E K U v = 0
mgh U initial h final initial E E 2 2 mv mgh gh v 2 2 2 mv K final Example: A roller coaster starts out at the top of a hill of height h . How fast is it going when it reaches the bottom? Example: An object of unknown mass is projected with an initial speed, v 0 = 10 m/s at an unknown angle above the horizontal. If air resistance could be neglected, what would be the speed of the object at height, h = 3.3 m above the starting point?

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## This note was uploaded on 10/21/2010 for the course PHYS 221 taught by Professor Herrera-siklody during the Fall '08 term at Iowa State.

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lecture15 - Gravitational potential energy Conservation of...

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