I am having some trouble calculating the kinetic energy of an impact between two objects. The formula is simple:
I am confused as to how to convert this energy into a damage value when both objects are moving. If one object is stationary and the other is moving at 20 meters per second, the formula above gives
1/2mass20^2 = 200mass joules
but if we simply change the frame of reference we get new values for the kinetic energy. For example, if both objects are instead traveling at 10 meters per second towards each other, they’d each have a kinetic energy of
1/2mass10^2 = 50mass joules
for a total of 100*mass joules when added together. I cannot wrap my head around why this happens. There shouldn’t be a difference in the impact between two cars crashing head-on while going at 50km/h each, and a stationary car being hit by another car moving at 100km/h. How can kinetic energy depend on the square of the velocity? How do I define 0 velocity?
Is there some better way of calculating the “damage” caused by an impact? This is obviously for a game, so I’m looking for plausibility, not 100% realism here.