Force, mass and acceleration | Movement and forces | Middle school physics | Khan Academy

So, I have three different asteroids over here, and they have different masses. We'll talk a lot more about what mass means, but one way to think about it is how much stuff there is there. There are other ways to think about it.

Let's say that this first asteroid is twice the mass of either of these two smaller ones, and these two smaller ones have the same mass. Now, we've attached the back of a rocket to each of these asteroids. In fact, this one over here has two rockets, and we're going to assume that all of the rockets are equivalent, and we ignite them all. So, they all exert the same force each on the asteroid.

For example, we have a net force acting leftward on this large asteroid. We have the same net force acting on this smaller asteroid, also going to the left. On this other smaller asteroid, we have two times that net force acting to the left. So, what I want you to do is pause this video and think about which of these asteroids is going to be accelerated the most and which of these asteroids is going to be accelerated the least.

Alright, so you might have an intuition that the larger the force, the more acceleration you might see. So, let me write it like this: you might get a sense that if you increase your force, that's also going to increase your acceleration. It does turn out that that is indeed the case.

Now, the other notion that you might have is that the more of the stuff that there is, the more mass that you have, the harder it is to accelerate it. So, if your mass is larger, then your acceleration is lower. It turns out that these things are all proportional. For example, if we just compare these two masses right over here, they have the same net force acting on them.

I keep saying net force; that means you just net out all of the forces acting in a certain dimension. For example, if I had another identical rocket acting in the opposite direction, they would net out, and this asteroid right over here wouldn't be accelerated at all. But going back to our example here, we have the same net force acting on each of these asteroids, but the first asteroid has twice the mass of the second asteroid.

So, how do you think the accelerations will relate? Well, as you might imagine, the acceleration on the larger asteroid is going to be half the acceleration on this asteroid. Or another way to think about it, this asteroid is going to have twice the acceleration as this first asteroid, and that's because it has half the mass.

One way you can relate force, mass, and acceleration—and this is one of the most important equations in all of physics—is that force is going to be equal to mass times acceleration. Or I could say the magnitude of the force is equal to the mass times the magnitude of the acceleration.

So notice in this example right over here, our forces are the same, but the masses are different. If I have half the mass as I have over here, I'm going to have twice the acceleration. That might make intuitive sense if you've ever tried to apply the same force to something that has a small mass versus something that has a large mass.

Now, if we compare these two asteroids, they have the same mass here, but the force here, the net force acting in that left direction, is double. So, if you double the force but don't change the mass, then you're going to have twice the acceleration. This is going to have twice the acceleration of this one, and this one's going to have twice the acceleration of that one.

But the important thing to realize is how force, mass, and acceleration are connected.