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    Engineering Physics
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SUMMARY

The discussion focuses on the dynamics of a hollow cylinder with mass M and radius R, which unwinds a cable attached to a block of mass m as it falls from a height h. The derived speed of the block upon reaching the floor is v=sqrt(2mgh/(m+M)). This differs from the speed of a solid cylinder, v=sqrt(2gh/(1+M/2m)), due to the distribution of mass and the moment of inertia affecting the energy conversion during the fall. The analysis emphasizes the application of energy concepts to understand these differences in speed.

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arabianights
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We wrap a light, flexible cable around a thin-walled, hollow cylinder with mass M and radius R. The cylinder is attached to the axle by spokes of a negligible moment of inertia.The cylinder rotates with negligible friction about a stationary horizontal axis. We tie the free end of the cable to a block of mass m and release the object with no initial velocity at a distance h above the floor. As the block falls, the cable unwinds without stretching or slipping, turning the cylinder. The speed of hanging mass m just as it strikes the floor is v=sqrt 2mgh/(m+M). Use energy concepts to explain why the answer to part A is different from the speed found in case of solid cylinder,which is
v= sqrt 2gh/(1+M/2m) ?
 
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