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

Question

A scene n 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 12.23 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 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 sate using the proposed mattress?

Explanation / Answer

Here we have to apply the conservation of energy(potential energy)
P.E before falling = P.E after falling(at the maximum compression distance)
mgH = kx2/2

=> m = kx2/2gH

here ,

g = 9.8

m = mass of the man

H= height of the floor + maximum compression on the spring

k = spring constant

x = maximum compression on the spring

m = 12.94 kg

Since the maximum mass the matress can support is only 12.98 kg , it is not safe.

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