4 ms·
> Putting it in somewhat fuzzier terms, and at the risk of repeating myself: F = ma derives its power from the (implicit) assertion that there is a simple unver
by knzhou 7y ago
> Putting it in somewhat fuzzier terms, and at the risk of repeating myself: F = ma derives its power from the (implicit) assertion that there is a simple unversal force law that lets us figure out F for a particular configuration of matter. And so the configuration of matter completely determines the acceleration of a test particle. There is no a priori reason this ought to be true. It’s an absolutely incredible fact of nature.
Yup, this is totally correct. To say it yet another way, we evaluate scientific theories not by looking at the pieces in isolation, but how much explanatory power you get from all the pieces working together (penalized by the total complexity of those pieces). There's nothing mathematically inconsistent about defining "F = mv", it just makes F a less useful quantity.
Feynman actually had a remarkably similar discussion in his classic lectures:
> For example, if we were to choose to say that an object left to itself keeps its position and does not move, then when we see something drifting, we could say that must be due to a “gorce” — a gorce is the rate of change of position. Now we have a wonderful new law, everything stands still except when a gorce is acting. You see, that would be analogous to the above definition of force, and it would contain no information.
> The real content of Newton’s laws is this: that the force is supposed to have some independent properties, in addition to the law F = ma. [...] It implies that if we study the mass times the acceleration and call the product the force, i.e., if we study the characteristics of force as a program of interest, then we shall find that forces have some simplicity; the law is a good program for analyzing nature, it is a suggestion that the forces will be simple.
- analog31 7y agoIn a lot of problems, there is a "F = mv" as well, just not using the letter m. A velocity dependent force is a "damping" force. Pushing an object through some fluid medium will produce damping. There is also a "F = mx" which is a spring return force. All three of these forces operating together drive the (approximate) equation of motion for a lot of mechanical things, such as the cone of a loudspeaker.
- semi-extrinsic 7y agoThose F's aren't the same as the one in "F = ma" though. The one in "F = ma" means "the (vector) sum of all forces on the object". You can write down, as you say, a bunch of contributions like F_spring and F_damp etc. that can be functions of other variables like x, v etc. "F = ma" then tells you that if you sum up all the forces (F_spring, F_damp etc) you have an expression for the acceleration. This gives you an equation of motion that you can solve to find out how the object will move given some initial state. Basically, if you know the initial position and velocity, you can compute acceleration at that time. Then you can figure out the position and velocity of the object a short time later, and recompute the acceleration using these new values. Then you can step forward again, and again, for as long as you want.
- pdonis 7y agoYou are describing ways in which the force depends on the configuration of matter. That is separate from how the total force--the sum of all the different forces that depend on different aspects of the configuration of matter--determines the acceleration.
- Chinjut 7y agoMan, yours is the only comment on this entire page that understands the central point of the linked article.
- wallace_f 7y ago>Feynman I like Feynman's analogy of physical laws to a chess board. >"Every once in a while we get to peak at the board," 'but we don't really know the rules driving the game, we're just trying to figure them out.'