What role does force play in a self-defense blow?

My self-defense instructor encouraged me hit the dummy with more force, so I exerted more force on my arm and it accelerated more rapidly. Yea for physics! But how does my increased force on my own arm cause me to hit the dummy with more force? — RL

Suppose you’re defending yourself against an attacker and you find that you have to hit them, either with your hand or with your fist. Two of the most important features of the impact between your hand and the person are how hard you push on the person and for how long.

The technical term for that push on the other person is a force; you exert a force on the other person. And a force is one of those physical quantities that has a direction to it. You can exert a force on someone toward the right or you can exert a force on someone toward left. Direction matters. Another thing about forces is that they’re always exerted between two thing, for example, you pushing on the other person. Forces don’t just exist by themselves; you can’t carry a force with you. You exert a force on something else.

That leaves this intuitive notion that you carry something with you during the wind up to an impact a little fuzzy. What is it you’re caring if you’re not carrying a force? Well, there is something you’re carrying: it’s known as momentum and momentum is a conserved physical quantity. That means you can’t create momentum or destroy momentum; all you can do is move it from one object to another.

In this respect momentum resembles money. Money is a conserved quantity, too, assuming that you don’t print it up in your basement (you are a law-abiding citizen) or you don’t destroy it (you’re not goofy). Money is conserved and goes from person to person to person. It is the conserved quantity of finance. Correspondingly, momentum is the conserved quantity of motion.

If you want to start moving to the right, you I have to accumulate some rightward momentum. Momentum, like force itself, has a direction to it. There’s momentum to the right; there’s momentum to the left. They are different, so if you want to move to the right, you have got to accumulate rightward momentum. The same is true of your hand or your fist, when you’re going after that attacker. If you want your fist to be really quick and move to the right rapidly, you have to invest a lot of rightward momentum into your fist.

To do that, you have to get that momentum from somewhere because you can’t make it. You can’t just cooking it up from nowhere. It comes from the ground and from the rest of your body. You pour rightward momentum—let’s suppose the bad guys are over to your right—you pour rightward momentum into your own fist. That momentum comes out of the rest of you and you do this how? By exerting a rightward force on your own fist.

You can do this—you can think of yourself as two separate parts: (1) your overall body and maybe your shoulder, and (2) the rest of you, your arm and your hand. So you’re pouring rightward momentum into your fist, at the expense of everything else. You actually can end up going backwards if you’re not careful

So you pour the rightward momentum into your hand and the amount of rightward momentum your hand accumulates is equal to the force you exert on your hand times the time over which you exert that force. The harder you push your hand and the longer you push your hand, the more rightward momentum it accumulates. If you want a fierce impact, You want to put a lot of rightward momentum into your hand. That means you push hard and you push long. You don’t go gently; you get going! You pour the momentum in so that its all accumulated.

This is this is the case not just for for punching somebody. It’s also the case for throwing a baseball. If you really want it to go fast, you need to take a long windup and you pour the rightward momentum into the baseball over as long a distance and with as much force as you can summon. Pack it full of rightward momentum, and off it goes. The same with a hammer. You pour rightward momentum into it, get it going and pack it full of momentum. When it hits the nail, its going to pack a wallop.

Okay, so now on to the impact. You have invested momentum in your hand; now when your hand hits something, it invests momentum in what it hits: the other guy, the bad guy. Your hand, which is chock-full of rightward momentum impacts that other person and transfers much or maybe even all its rightward momentum to that person by way of a force for a time. It’s passing along that momentum and it turns out that it can pass all of its momentum in a variety of different patterns. It can either pass along all its momentum with a gentle force over a long time, by pushing the person as they go away, or it can transfer all its momentum with a giant force for a short time.

If you hit knuckles to jaw, that impact is fierce and involves a big force, but not for very long. All the moment goes over in a jiffy. So a momentum transfer, it turns out, the amount of momentum you the put into something or transfer to something, is just this product of force times time. You can use a little force for a long time, or a big force for a short time; both of them can transfer the same momentum.

Well, if you really want to stun somebody, you want to make the transfer quick—short time, big force—and so that’s the bare-knuckle fight. It hurts. On the other hand, if you put on big fluffy gloves and delay or prolong the impact, it’s a little force for a big time. It more pushes you, but it doesn’t have that peak impact force that hurts.

So there you have it: if you’re trying to defend yourself against an attacker and you punch them, you do it by accumulating as much momentum toward the bad guy as possible. Use a big force for a big time, whatever you can do to get a lot of forward momentum into your knuckles and into hand. At the impact point—the moment when when you touch the other person—you want to transfer all that momentum to the other person, perhaps by way a big force for a short time. That’ll hurt everybody involved, you included, but, in any case, hopefully it will have the desired effect of getting the bad guy to go away and leave you alone.