Ah; I see what you’re driving at now. I still think you’re wrong, however. First, let’s seperate the problem into two cases:
The projectile (say a tennis ball) is hitting the surface of your body. I think this is what you are referring to. In this case the force exerted by the projectile also depends on the flexibility of the place it hits. More flexible = more springy = greater indentation for a given force. Let’s call the measure of this flexibility (1/k), where k is the stiffness. If you make some simplifying assumptions, you find that the force applied is proportional to vsqrt(km), and the time is proportional to sqrt (m/k). Multiply those out, and Ft = mv (as it should). More importantly, projectiles with the same energy but different momenta (as in your earlier example, where projectile B has 4m and (1/2)v) will have the same force parameter - note force is proportional to sqrt (energy) - but the time it takes to decelerate will be different, taking longer for higher mass. So still, the important parameter, force, is a function of energy rather than momentum.
The projectile (say a bullet) is actually plowing through your body This is what I was talking about earlier, and what I thought you were talking about in your first post. In this case, force is determined by what it takes to break apart the material the projectile is passing through. This will depend on the tissue itself , and the volume and shape of the bullet (in the simplest case), but not its mass or velocity.
One mistake some people are making here is assuming the projectile must actually be stopped by your body. If the question is regarding a thrown object (e.g. a bowling ball), you have to allow for the possibility that it moves you, losing some energy in the process.
Also, the mack truck analogy invites the complaint about the differing surface areas, but it holds up even with the same surface area. Stick a pole with a billiard ball on the end on the front of a slow-moving truck, and I’d much rather be poked with that than with a billiard bill that has the same momentum. It’ll knock me down, and I have no hope of actually *stopping * the thing, but it wont really hurt me.
But considering the original question "If I’m hit by thrown object, is it momentum or energy that I want to minimize? " Is it not a little late to try to minimize either momentum or energy once you have been hit by a thrown object? Considering it already hit you? On a serious note it seems to me that this is a trick question. It is impossible to consider (the correctly stated question) without knowing the value of some other variables. Namely Mass and velocity.
Believe me, it is not a trick question; your grammar and syntax have no effect on me!
Before I had heard of impulse I had figured that you have momentum and energy and that they moved differently because of their functional forms. I had often heard that when punching, doing so quickly was more effective than putting a lot of muscle behind it—to the extent that those can be separated—but then again Roy Jones, Jr. talked about lunging for a knock-out punch so that your body weight is behind it. Elsewhere I have heard that punching power comes from the hips, not a fast extension of the arm.
And, of course, there is the carnival game where one strikes the what-ever-it’s-called with a sledge hammer and the plug rides up and (hopefully) strikes a bell. The fmr. carnie I knew said that all sorts of muscle men would confidently attempt and fail, but he got it every time because they were hitting it hard, while he was hitting it fast.
Obviously I’ve concluded that “depends” is going to be the first answer to the question. However, I don’t think that it is too much to abstract away a bit and talk about why one vs. the other matters more under such-and-such general conditions. Which posters have done. This has been a very satisfying, albeit frusterating (sp?), thread.
On a serious note it seems to me that this is a trick question. It is impossible to consider (the correctly stated question) without knowing the value of some other variables. Namely Mass and velocity.