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.
"Does it matter? What matters in a collision, the energy, the momentum, or both"
'Rule of thumb' is: momentum for penetration, energy for damages.
It's easy to illustrate: just look at bullets.
I would think that penetration would depend on energy. If you assume a constant force acting on the bullet (or object) while it is interacting with the material, then you could think about work as W = Fd = change in kinetic energy.
But, if that is the rule of thumb then it must be based on experience.
I don't think you can take such a shortcut, you'd have to work out the collision in at least some detail. In any case even with a tornado wind at 300mph, it is unlikely a solid object picked up by it would be traveling that fast. There should be a rough time constant during which an object in a fluid will come to have the same velocity of the fluid. I would bet that time is longer than the time for the tornado (vector) wind velocity to remain constant.
The answer is almost certainly 'neither' or perhaps 'some combination of both'. The penetration of a chunk of glass will be driven by both the work required to cut through the neck (linear in energy) and the energy wasted by fluid dynamics interactions with tissue (generally second order in velocity and thus actually scaling with sectional density, not energy or momentum).
"But, if that is the rule of thumb then it must be based on experience."
Yes. In essence, this rule of thumb means that among the projectiles of the same energy a projectile with the largest momentum generally has best penetration power.
And among the projectiles with the same momentum, a projectile with the largest energy generally inflicts more damage.
A scaling complication is that the materials are not linear. Tendons and other biological material respond differently in different time frames. They might fail by tensile tearing at low speed, and by transverse cutting at high speed.
The geometry of the glass edge is also a factor which might not be linearly scalable. A thin, sharp edge will blunt (melt?) during a high-speed cut. A thick edge will retain its geometry at higher speeds.
"...and through it at a simulated human neck"
Through it? Is that an attempt to combine "throw it" and "through the neck"?! Hey it could catch on....
excellent work, ive just finished my kinetic energy paper but ill update with the maths thanks.