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problem10_73

University Physics with Modern Physics with Mastering Physics (11th Edition)

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10.73: Find the speed v the marble needs at the edge of the pit to make it to the level ground on the other side. The marble must travel 36 m horizontally while falling vertically 20 m. Use the vertical motion to find the time. Take y + to be downward. m/s. 82 . 17 gives Then s 02 . 2 gives ? m, 20 , m/s 80 . 9 , 0 0 0 0 2 2 1 0 0 0 2 0 = = - = + = - = = - = = x x y y y y v t v x x t t a t v y y t y y a v Use conservation of energy, where point 1 is at the starting point and point 2 is at the edge of the pit, where m/s. 82 . 17 = v Take 0 = y at point 2, so . and 0 1 2 h y y = = 2 2 1 2 2 1 2 2 1 1 ϖ I mv
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Unformatted text preview: U K U K + = + = + Rolling without slipping means 2 5 1 2 2 1 2 5 2 so , . mv I mr I r v ω = ϖ = = m 23 ) m/s 10(9.80 m/s) 82 . 17 ( 7 10 7 2 2 2 10 7 = = = = g v h mv mgh b) , 2 5 1 2 2 1 mv I = Independent of r. c) All is the same, except there is no rotational kinetic energy term in 2 2 1 : mv K K = 2 2 1 mv mgh = 0.7 m, 16 2 2 = = g v h times smaller than the answer in part ( a)....
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