Philosophy 167: Class 8 - Part 11 - The Third Law of Natural Motion- Descartes' Account of Impact.
Smith, George E. (George Edwin), 1938-
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The third law of motion. This is very different. When a body meets another, if it has less force to where it is vim, the same word Newton uses. Less force to continue to move in a straight line. Then the other has to resist it it is turned aside in another direction.
Retaining its quantity of motion. And changing only the direction of motion. If however it has more force, it moves the other body with it. And loses as much of its motion as it gives to that other. Okay. Now the version in Lamont. When one of these bodies pushes another.
It can not give the other any more motion except by losing as much as its own at the same time. Nor can it take away from the other body's motion unless its own is increased by as much. And here, just as before, motion is bulk times speed. So what's the idea here?
We've got an earlier principle that total quantity of motion in the universe is a constant. Two bodies collide. They change their motion. There's nothing in principle that prevents that being compensated for somewhere else, to keep the total motion the same. Right? So this is, in effect, saying all changes in motion are local, it's a localization principle.
The reason all the, not the reason, what enables all the motion to be conserved is that all changes of motion involve conserving of motion transfer one from the other. That's the idea. So it's not as trivial as it looks, though of course it's gonna turn out to be wrong.
It's not gonna turn out to be as wrong as I'm gonna make it appear in the next few minutes. But the basic idea of what happens causally in any change of motion has to be some form of transfer of motion from one body to another. Now, he knew about it gunpowder, he knew about things like that.
So exactly, well, his theory of fire, etc., was a very rapid motion. So maybe he can give an account. I don't remember in part four what he says about gunpowder. I mean, he really thinks he can give a solution to everything in terms of motion. So, that's the remark I make down here though, that it's a matter of local change.
And he has two cases. Perfectly elastic reflection with no change in the amount of motion of either bodies in contact and transfer of motion. Transfer of the quantity of motion from the body, from one body with the greater force to resist. To the body and contact with it.
And this idea of a force to resist motion, you'll see it again in Newton's Principia, interesting enough, he talks about the force of inertia, and it's not hard to understand. Go try to push a train down the tracks with your bare hands. And you'll notice it has a lot of force to resist.
A lot of capacity to resist. Other bodies have less. And if there's a transfer of motion, therefore, there's gonna have to be a very large transfer of motion from you to that train to get it moving because it's so huge. That's the sort of thing that he has in mind.
He's not crazy. But what it leads to is gonna look crazy. So let's see what he says about on impact. In order to determine from the preceding laws how individual bodies increase or decrease their movements or turn aside in different directions because of encounters with other bodies. It is only necessary to calculate how much force to move or to resist movement there is in each body.
Now that's an interesting problem, right? We've got to quantify that amount of force and we then have to be able to calculate it. And to accept as a certainty, that the one which is stronger will always produce its effect. Moreover, this could easily be calculated if only two bodies were to come in contact, and if they were perfectly solid and separated from all others.
Both solid and fluid, in such a way that their movements would be neither impeded nor aided by any other surrounding bodies. For then they observed the following rules. All right, I'm gonna turn to the rules in a moment. Anybody who's had an elementary physics course has had the issue of what happens when one sphere impacts another sphere head on.
And what they teach you to do is write this equation down. The only difference is the word bulk molus is replaced by the English mass, Latin massa. So bulk times speed of body one plus bulk time speed of body two. And that's directional. It has to be equal before to the product afterwards, okay?
But now the crucial thing to notice here, there are two unknowns in one equation. This is inadequate to solve the problem of what happens when two spheres impact. What they teach you in physics courses is, well there's a second principle, the sum of nv squared is also preserved before and after.
I always laugh when they call that conservation of energy. Energy is a term that got introduced in the 1840s. So, but that's beside the point, what I always like to laugh at is to solve that little, tiny problem of two spheres colliding with one another. We need two of the most fundamental principles in all of physics, conservation principles, conservation of momentum, conservation of physics.
How are you gonna prove those so that you can solve his local problem of two spheres. Of course, in physics books they don't tell you how to prove conservation of momentum and conservation of energy. They tell you it's true and show you, if you divide this one into the other one, you get the solution.
You'll see the solution not done that way and not invoking any conservation principle whatsoever by Huygens week after next. It's one of the very, very beautiful, many beautiful things he did. But it's just, Descartes rightly looks at this and says, okay, I need another principle to determine what happens afterwards from before, because I've got too many possibilities from this principle alone.
Okay. We'll turn to his rules in a moment. Now, I'm very worried about this question of how to measure the excess force on body i. Is it simply the change in bulk time speed that is the force to be equated with the change in motion? He doesn't tell us anything else.
It would seem to have to be. Because it's the excess of force to resist or to change motion that allows it. In fact that's the way he thinks about this. This is a competition between two bodies, each of which has its own, inherent force, an inherent force to resist change of motion.
And the one with the larger inherent force wins the contest. Okay. That's the form in which he initially conceptualizes it. That's not enough to tell you what happens afterwards. However that's only enough to tell you which one is dominant in the two.