You are the technical consultant for an action-adventure film in which a stunt c

Question

You are the technical consultant for an action-adventure film in which a stunt calls for the hero to drop off a 24.9-m tall building and land on the ground safely at a final vertical speed of 3.81 m/s. At the edge of the building's roof, there is a 131-kg drum that is wound with a sufficiently long rope (of negligible mass), has a radius of 0.393 m, and is free to rotate about its cylindrical axis with a moment of inertia I0. The script calls for the 59.5-kg stuntman to tie the rope around his waist and walk off the roof.

a) Determine the required value of the stuntman's acceleration if he is to land safely at a speed of 3.81 m/s, and use this value to calculate the moment of inertia of the drum about its axis.

b) What is the angular acceleration of the drum?

c) How many revolutions does the drum make during the fall?

Explanation / Answer

a] M A H = .5 M V^2
b] Knowing Vsplat gives you the angular velocity [rotation rate] of the drum, since the rope moves at the rim velocity. Knowing final rotation rate [and initial = 0] and time [from D = .5 A t^2] fives you angular accel
c] circumference x revolutions = length of rope reeled out = height [22.1 M]

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