In the last episode of MythBusters, they wanted to see if a tornado could make some glass cut off a person’s head. The first attempt was just to take some glass and through it at a simulated human neck. Clearly, this wasn’t quite the same as a tornado.
So, here was their plan. If they want to simulate glass moving at 300 mph, they could get a bigger piece of glass and put it on a truck moving at 80 mph. The result would give a piece of glass with the same kinetic energy as a smaller piece moving at 300 mph. Their calculations look to be correct. However, the question is: would this make the same type of collision?
Let me just write an example. Suppose I want to simulate a 2 kg piece of glass moving at 100 m/s. This would have a kinetic energy of:
Now, what if I want an object with the same kinetic energy, but just moving at 1/4th the speed of the original object, but with a larger mass?
If you want it to go 1/4th as fast, it would have to be 16 times more massive. Now, here is the possible problem. What about momentum? Here is the momentum of these two objects (well, the magnitude of the momentum)
Not the same momentum. Now, here is the real question. Does it matter? What matters in a collision, the energy, the momentum, or both? I am not really sure of the answer in the case of a decapitation. I am thinking only the energy matters (but I am ok with the possibility that I am in correct). Why would I say this? In this particular situation, the MythBusters have the fake neck attached to some holder. During the collision, there momentum will not be conserved because there is an external force (from the ground) on the fake-neck. So maybe it doesn’t even matter that the momentums are not the same.
Now, if this were a collision between two free objects I think the momentum would be important.