|This post is about physics. You may want to not bother.|
So, I've been arguing in the comments of someone else's livejournal. The dispute is me saying that a car at 110mph colliding head-on with a stationary car is an equivalent impact to a car at 55mph colliding head-on with another car going the opposite way at 55mph. The other person is arguing that a car going at 55mph has 313kJ of kinetic energy, and a car going 110mph has 1252kJ of kinetic energy, so the collision at 110mph must be more severe. (1252 > 313+313)
I was frankly surprised that he would believe this because it's self-evident to me that he is wrong, from two or three distinct physics approaches that all agree - but he's not a stupid guy, and I couldn't immediately explain why he is wrong, only why I am right. His math is right, and kinetic energy is proportional to velocity squared. After a little research I found the answer, and after a bit of argument also found why he was so fixated on the wrong answer - because it has been argued a lot with a slightly different situation, in which he would be right. A 55mph car colliding head-on with another 55mph car is not equivalent to a 110mph car hitting a wall. It is, in fact, equivalent (for the car's occupants) to a 55mph car hitting a wall. But it is also equivalent to a 110mph car hitting a stationary identical car.
But how and why is he wrong about the kinetic energy? I'll explain it in comments later if anyone is interested and nobody else has explained it.