Question

A person weighing 180 lbs falls from a tree and hits the ground at 20 mph. There is a foam pad in between the human and ground with thickness=5" and stiffness=K. Find the optimum value of K to reduce acceleration (or shock) witnesses by the human.

Answer 1

Covert all the units in SI units.

Mean, velocity in m/s and length in meters.

m = 180 lbs = 81.6 kg

Speed, v = 20 mph = 8.94 m/s

thickness, x = 5" = 0.127 m

Solve this problem by using conservation of energy.

Kinetic energy of the person just before striking the foam pad = (1/2)*m*v^2 = 0.5*81.6*8.94^2

And this must be equal to the spring energy = (1/2)*K*x^2

So -

0.5*81.6*8.94^2 = 0.5*K*0.127^2

cancel '0.5' from both sides.

K = (81.6*8.94^2) / 0.127^2 = 404350 N/m = 404.35 kN/m