Modern bowling alleys have automatic ball returns. The ball is lifted to a heigh

Question

Modern bowling alleys have automatic ball returns. The ball is lifted to a height of 2.40 m at the end of the alley and, starting from rest, rolls down a ramp. It continues to roll horizontally and eventually rolls up a ramp at the other end that is 0.500 m off the ground. Part A: Assuming the mass of the bowling ball is 7.00 kg and its radius is 19.0 cm , determine the rotation rate of the ball during the middle horizontal travel Part B: Determine it's linear speed during the middle horizontal travel. Part C: Determine the final rotation Part D: Determine the final linear speed

Explanation / Answer

assuming frictionalless surface mgh = 0.5*I w^2 7*9.8*2.4 = 0.5* 2mr^2/5 * w^2 7*9.8*2.4 = 0.5* 2*7*0.19^2/5 * w^2 w = 57 rad/sec v = wr = 57*0.19 = 10.84 m/sec mgh1 = mgh2 + 0.5*I*w2^2 7*9.8*(2.4-0.5) = 0.5* 2*7*0.19^2/5 * w2^2 w2 = 50.78 rad/sec v2 = w2*r = 50.78*0.19 = 9.64 m/s

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