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 if effectively has a spring constant of 77144 N/m for the area likely to be impacted by the stuntman, but cannot depress more than 13.55 cm without injuring him. To approach this problem, consider a simplified version of the situation. A mass falls through a height of 3.72 m before landing on a spring of force constant 77144 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? Warning: 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

Given that the spring constant is k = 77144 N/m Height above the spring is h = 3.72 m compressed length of the spring is x = 13.55 cm = 0.1355 m ----------------------------------------------------------------------- Apply conservation of energy to the system,           mgh = (1/2)kx2 - mgx      mg(h+ x) = (1/2)kx2              m =  kx2 / 2g(h +x)              m = 18.72 kg No, Stunt not safe using this arrangement.            Given that the spring constant is k = 77144 N/m Height above the spring is h = 3.72 m compressed length of the spring is x = 13.55 cm = 0.1355 m ----------------------------------------------------------------------- Apply conservation of energy to the system,           mgh = (1/2)kx2 - mgx      mg(h+ x) = (1/2)kx2              m =  kx2 / 2g(h +x)              m = 18.72 kg No, Stunt not safe using this arrangement.                         m =  kx2 / 2g(h +x)              m = 18.72 kg No, Stunt not safe using this arrangement.              m = 18.72 kg No, Stunt not safe using this arrangement.           

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