How big is the force that a falling bowling ball hits you with? [painfull]

Ask A mathematician explains in a joyful manner how much force is involved when a falling bowling ball hits your toes. As painful as it is we have to do a bit of math to see what energies are at work in there.

As you know Energy = Work = Force * Distance. Since the energy is conserved the energy of the falling ball needs to be equal to the energy of the ball that is stopped by your foot and thus: Ff * Df = Fs * Ds, the lowercase f means “fall” and s means “stop”.

What does the physicist say? This:

So, if you drop a 10 pound ball 4 feet (48 inches), and it stops in a quarter inch, then the force at the bottom of the fall is F = 48/0.2510lbs ~ 200lbs. This is why padding is so important; if that distance was only an eighth of an inch (seems reasonable) then the force jumps to 400lbs, and if that distance is increased to half an inch then the force drops to 100 lbs.

Science can be toe-crushingly fun :))

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