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Unformatted text preview: A hollow spherical ball of mass m and of radius r is rolling back and forth in the bottom of a bowl in the shape of a hemisphere of radius R . You can assume that r ± R . (a) Write an expression for the total energy E of the ball as function of ± , the distance of the ball from the bottom of the bowl as measured along the bowl, and v the speed of the ball. (b) What is an approximate expression for E when ± is very small? (c) By comparing with the total energy E for a mass on a spring, calculate the period of this motion. Check the units of your ±nal answer. Problem 9 1 By plugging into the diferential equation For a damped mass on a spring, m d 2 x dt 2 =kxb dx dt veriFy the solution: x ( t ) = A ebt/ 2 m cos( ω ± t + φ ) where ω ± = ± k/mb 2 / 4 m 2 . 2...
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 Fall '07
 LECLAIR,A
 Kinetic Energy, Mass, 2 sec, 1Kg, 2m, 3 m, 2 m/s

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