For a stunt in a movie, an actress falls through a hole in a floor onto the bed

Question

For a stunt in a movie, an actress falls through a hole in a floor onto the bed in the bedroom below. The mattress on the bed effectively acts like a spring for the area likely to be impacted by the actress, but it cannot compress more than a certain distance without injuring her. To determine if the fall will injure her. you need to calculate the largest mass that can fall on the mattress without exceeding this maximum compression distance. Here are the assumptions you can make. 1) The mass falls through a height of 3.72 m before landing on the bed (the same height the actress will fall). 2) The mass will then compress the mattress by 12.89 cm (the maximum compression allowed before injury). 3) The mattress's spring force constant is effectively 65144 N/m. Largest mass that can safely fall on bed Based on this crude estimate, is the stunt safe? The average mass for an adult is roughly 62 kg

Explanation / Answer

1)

h = height above the bed = 3.72 m

x = compression of the spring = 12.89 cm = 0.1289 m

k = spring constant = 65144 N/m

m = mass

using conservation of energy

potential energy = spring potential energy

mg (h + x) = (0.5) k x2

m (9.8) (3.72 + 0.1289) = (0.5) (65144) (0.1289)2

m = 14.35 kg

since the average mass 62 is way greater than the maximum safe mass of 14.35 kg , hence the stunt is not safe at all

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