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 a researcher has been hired to investigate the safety of this stunt. When the researcher examines the mattress, she sees that it effectively has a spring constant of 65144 N/m for the area likely to be impacted by the stuntman, but it cannot depress more than 11.79 cm without injuring him. To approach this problem, consider a simplified version of the situation. A mass falls through a height of 3.12 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.

Answer 1

14.27 kg

Step-by-step explanation:

Potential energy of the body falling from the height = mg (h +e) where m is the mass of the body in kg, g is acceleration due to gravity in m/s² and h is height in m

energy conserved in the mattress by the body falling on it = 0.5 k e² where e is the compression of the mattress and k is the force constant

Potential energy = work done in compressing the mattress to 11.79 cm

m g(h+e) = 0.5 k e²

m = 0.5 k e² / g(h+e) = ( 0.5 × 65144N/m × (0.1179 m)²) / ( 9.8 m/s² × (3.12m+ 0.1179m) = 14.27 kg