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## Middle school physics - NGSS

# Force, mass and acceleration

NGSS.MS:

MS‑PS2

, MS‑PS2‑2

, MS‑PS2.A.2

, MS‑PS2.A

When a net force acts on an object the object's motion will change in the direction of this net force. The larger the force is that acts on an object, the larger the change in motion. However, the greater the mass of the object, the greater the force needed to have the same change in motion.
Created by Sal Khan.

## Video transcript

- So I have three different
asteroids over here and they have different masses. And 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's other ways to think about it. And so 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. And so they all exert the same
force each on the asteroid. So 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. And 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. All right. So you might have an intuition
that the larger the force, the more acceleration you might see. So let me write it like this. So you might get a sense that
if you increase your force, that that's also going to
increase your acceleration. And 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 you're mass is larger, than your acceleration is lower. And it turns out that these
things are all proportional. So for example, if we just compare these
two masses right over here, they have the same net force acting on it. And 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. And 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. And 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,
don't change the mass. Well, then you're going to
have twice the acceleration. So 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.