Two pulleys, one with a radius 2R and one with a radius of R, are welded together and can rotate about the same axis. A block is suspended from a string that is wrapped around the small disk and unwinds without slipping as the block descends a distance H and reaches a certain final speed. If the string with the block at the other end were wrapped around the larger disk, how would the final speed of the block change?

Question

Physics

Broderick Clay

17 October, 20:35

Two pulleys, one with a radius 2R and one with a radius of R, are welded together and can rotate about the same axis. A block is suspended from a string that is wrapped around the small disk and unwinds without slipping as the block descends a distance H and reaches a certain final speed. If the string with the block at the other end were wrapped around the larger disk, how would the final speed of the block change?

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Answers (1)

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Liana · Answer 1

speed will double

Explanation:

Tangential velocity is given by

v=wr

where r is radius and w is rotational velocity. When r is increased to 2R, keeping roational velocity constant, the tangential velocity doubles. Hence unwinding will take place at a twice the rate and the final velocity will be double