You are helping to esign a new fire escape for yourthird-floor apartment. You st

Question

You are helping to esign a new fire escape for yourthird-floor apartment. You step out the window onto a platform thatis attached to a rope, which in turn is wound around a massivesolid cylindrical flywheel. that can turn on its axis. As youfall a increasing speed, the rope causes the flywheel to turn atincreasing angular velocity. Your task is to choose a flywheel thatwill enable you to move at a safe 2.0 m/s when you reach th ground10m below your starting position. Your mass is 80kg. Determine therotational inertia and mass of the uniform 0.80 radius flywheel youneed to buy. Use work energy and/or impulse momentum to solve thisproblem. I need help with all of the steps to solving this homeworkproblem. Thank you. You are helping to esign a new fire escape for yourthird-floor apartment. You step out the window onto a platform thatis attached to a rope, which in turn is wound around a massivesolid cylindrical flywheel. that can turn on its axis. As youfall a increasing speed, the rope causes the flywheel to turn atincreasing angular velocity. Your task is to choose a flywheel thatwill enable you to move at a safe 2.0 m/s when you reach th ground10m below your starting position. Your mass is 80kg. Determine therotational inertia and mass of the uniform 0.80 radius flywheel youneed to buy. Use work energy and/or impulse momentum to solve thisproblem. I need help with all of the steps to solving this homeworkproblem. Thank you.

Explanation / Answer

v = 2.0 m/s, h = 10 m, m = 80 kg, r = 0.80 m find the rotational inertia I and mass M of the flywheel. I =Mr2/2 initial energy = mgh final energy = mv2/2 + I2/2 =mv2/2 + (Mr2/2)(v/r)2/2 = (m +M/2)v2/2 mgh = (m + M/2)v2/2 M = 2m(2gh/v2 - 1) = 7680 kg I = Mr2/2 = 2457.6 kg-m2

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