We wrap a light, nonstretching cable around a $8\mathrm{.}00$ kg solid cylinder with diameter of $28\mathrm{.}0$ cm $.$ The cylinder rotates with negligible friction about a stationary horizontal axis. We tie the free end of the cable to a $12\mathrm{.}0$ kg block and release the block from rest. As the block falls, the cable unwinds without stretching or slipping.

Part A

How far will the mass have to descend to give the cylinder $500$ J of kinetic energy?

Express your answer in meters.

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