QuestionDetails: The ball B has a weight of 5lb and is originally rotating in ac

Question

QuestionDetails: The ball B has a weight of 5lb and is originally rotating in acircle. As shown, the cord AB has a length of 3 ft and passesthrought the hole A, which is 2ft above the plane of motion . If 1.5ftof cord is pulled through the hole, determine the speed of theball when it QuestionDetails: The ball B has a weight of 5lb and is originally rotating in acircle. As shown, the cord AB has a length of 3 ft and passesthrought the hole A, which is 2ft above the plane of motion . If 1.5ftof cord is pulled through the hole, determine the speed of theball when it moves in a circular path at C.

Explanation / Answer

let v1 and r1 be the intial velocity of the ball andradius of the circular      centrifugal force is balanced by tehcomponent of te weight of the ball                mv1^2 / r1 = mgsin1          (sin1 = r1 / 3ft)                 v1 = g r1^2 / 3ft           simillarly after pulling the thread                mv2^2/ r2 = mg sin2                   v2 = g r2^2 /1.5ft           (sin2 = r2 / 1.5ft )             from the intial circle                      tan1 = 2 / 3 from which we can solve for 1           andhence r1 can be solved taking angular mometum to be constant                   v1 /v2 = r2 / r1 using the above relations we can sovle for 1 ,2 r1and r2 and hence v1 and v2     

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