We wrap a light, nonstretching cable around a $10\mathrm{.}0kg$ solid cylinder with diameter of $36\mathrm{.}0cm.$ The cylinder rotates with negligible friction about a stationary horizontal axis. We tie the free end of the cable to a $14\mathrm{.}0kg$ 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 $520J$ of kinetic energy?

Express your answer in meters.