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>> Hello, class. Professor Anderson here. Let's talk a little bit more about Newton's second law. We introduced this last lecture. Let's say we wrote down the following equation. Sum of the forces is equal to the mass times acceleration. And let's ask, let's ask the following question. If we double the force, what is our new acceleration? Okay? Pretty straightforward question. We have a relationship here between force and acceleration. So let's say we take an object, and we're going to push on that object, and we're going to give it a force F. That means it's going to accelerate with A. If I double that force, what happens to A? Anthony, what do you think? >> It increases because they're directly related. >> Yeah, they're directly related, right? If I push harder on this block, it's going to accelerate faster. If I double how hard I push on it, what's going to happen to the acceleration? Anthony, what do you think? >> It should also double? >> That's right. It will double, okay? So acceleration will also double. How do we see that mathematically? Well, we just have one force. So our summation just becomes that. F equals MA. And we're only worried about one dimension here. So let's just forget the vector signs for a second. F equals MA. Now, if I repeat the experiment and I double the force and I call that thing A prime, how do I rewrite this equation? Well, I double the force. So 2F equals M times A prime. And now I want to solve this thing for A prime. All right, what do I do? I have MA prime equals 2F. But I know what F is from my earlier equation. That's just M times A. And now I have one equation, MA prime equals 2MA. I can divide both sides by M, and I get A prime is equal to 2A. Absolutely. It doubles. All right, good. Now, that was for a given mass M. Let's try it slightly differently. We're not going to double the force. Let's double the mass. So if I double the mass, I keep the force the same. What is our new acceleration? What's your name right here? >> Tricia. >> Tricia. Tricia, what do you think? If I keep the force the same, but now I'm going to double the mass that I'm trying to push, is that acceleration going to be higher or lower? >> Lower. >> Lower, right. It makes sense, right? If you're pushing on the Honda Civic, and then all of a sudden you've moved over and you're pushing on the Cadillac, all right, which one is going to accelerate faster? The lighter one. The Honda Civic is, of course, going to accelerate faster. So we think it's going to be smaller. How much smaller do you think it will be, Tricia? >> Half? >> Okay, she's going to guess that it is halved. Let's see how we can do it mathematically. So there's our first equation. We're okay with that. Let's erase the second one. And now what we're going to say is all right, same force, but we're going to double the mass. And that leads to a new acceleration A prime. Can we solve this thing for A prime? Sure, A prime is F over 2M. We know what F is from the first one, MA over 2M. The Ms cross out, and I get A prime equals A over 2. Good. Piece of cake. Your guess was right on the money.

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