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 19-m-tall building and land on the ground safely at a final vertical speed of 3 m/s. At the edge of the building's roof, there is a 100-kg drum that is wound with a sufficiently long rope (of negligible mass), has a radius of 0.4 m, and is free to rotate about its cylindrical axis with a moment of inertia I0. The script calls for the 54-kg stuntman to tie the rope around his waist and walk off the roof.

(a) Determine an expression for the stuntman's linear acceleration in terms of his massm, the drum's radiusr, and moment of inertia

Explanation / Answer

1. Use vf^2 = vi^2 + 2ad to find his acceleration "a". With numbers we have: (3.93)^2 = 0 + 2*a*(22.1). Solving for a we have: a 0.349 m/s^2 2. Newton's Second Law applied to the stuntman: mg - T = ma. Solving for T (tension in the rope) we have T = 575.6 N 3. The equation for rotary motion of the drum : T*r = (Io)(angular acceleration) 4. The angular acceleration = a/r = 0.349/0.443 = 0.7878 rad/s. Plug this number in the above equation (Eq.3) and solve for Io. Equation 3 with numbers: (575.6)().443) = (Io)(0.7878). Solving for Io we have: Io = 324 kgm^2 (rounded to three significant digits)

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