Impact force of an object dropped on a steel toed shoe
I often hear about collisions in terms of impact force. For instance, "the boxer delivered a punch with 100 lbs of force." I have a pair of steel toed shoes that are rated to withstand 70 lbs of force (311 N). But if the shoe experiences an impact instead of being loaded very gradually, wouldn't it be more informative to talk about how much energy the shoe can absorb without failing?
I know that a falling 31.7 kg mass will experience a gravitational force of 311 N, but that is not equal to the force required by the shoe to stop the mass, correct? Because the shoe must dissipate the kinetic energy that the mass has acquired, and the magnitude of the required force depends on how the shoe applies that force (over what time period and what displacement).
Let's say we wanted to know how large of a mass we could drop from 5 meters high without having the shoe fail. It seems to me like we could not calculate this, because we do not know the details about how the shoe applies the force to the mass.
I've had three years of classes in undergraduate mechanical engineering, but I'm still trying to fully wrap my head around Newtonian physics. Any light you guys could shed on this would be awesome, thanks in advance for your help!