A scene in a movie has a stuntman falling through a floor onto a bed in the room

Question

A scene in a movie has a stuntman falling through a floor onto a bed in the room below. The plan is to have the actor fall on his back, but you have been hired to investigate the safety of this stunt. When you examine the mattress. you see that it effectively has a spring constant of 65144 N/m for the area likely to be impacted by the stuntman, but cannot depress more than 12.89 cm without injuring him. To approach this problem, consider a simplified version of the situation. A mass falls through a height of 3.52 m before landing on a spring of force constant 65144 N/m. Calculate the maximum mass that can fall on the mattress without exceeding the maximum compression distance. Based on this crude measurement, is the stunt safe using the proposed mattress? Yes No Cannot determine The safety of movie stunts is now heavily researched and involves more sophisticated computations than used here. Do not attempt stunts on your own.

Explanation / Answer

Consider that the mass m stopped with in a distance of d = 0.1289 m
Spring energy = Work done by gravity
1/2 kd2 = mgh
0.5 x 65114 x (0.1289)2 = m x 9.8 x 3.52
540.941 = 34.496 m
m = 540.941 / 34.496
= 15.68 kg

Since this mass is very less compared to the average mass of a person, the stunt is not safe.

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