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Solving Motion Problems with Forces

Patrick Ford
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Hey, guys. In earlier chapters, we saw how to solve motion problems using these four equations of motion right here in more recent videos, we start to see how to solve forces problems. We're gonna start to see some problems that are not going to combine forces and motion. So I'm gonna show you in this video of how we solve one dimensional motion problems with forces. And really, it's just using a combination of equations that we've already seen before. So let's go ahead and check this out. But first I want to recap what we've already seen in earlier chapters. Remember that your five motion variables are the initial the final Delta X, delta T and A. So we have these five motion variables, and as long as you know three out of those five and you can pick one of these three or four equations to solve a problem and then more recent videos, we started working with forces problems. Remember that there's only three variables, enforces problems that's f M and A, and there's only one equation to use. We use f equals M A, which means that you need to out of those three knowns in order to solve a problem. But now we're gonna start seeing problems that combine the two. You're gonna start seeing combinations of forced variables and motion variables. A diagram of that might look something like this where you have a mass that's being pulled, pushed by some force. It's going to accelerate. But you also have some initial velocity final velocity, Delta X or Delta T. So to solve these problems, we're just going to use a combination of these equations. We're just going to use a combination of f equals M A and are you AM or motion equations that we've already gotten super familiar with. So what I want you to do is look at these sets of variables here and you'll notice that's one. There's one that's common between them. You'll notice the A variable. The acceleration is the one that is shared between both sets. So that's how we're gonna solve these kinds of problems to show you how that works. I'm just gonna go right into this example down here. So if we look at this example, we've got this 20 kg block, so that's a mass. We know that the masses 20 it's on a frictionless surface that's being pushed, but it's accelerating and accelerating to 30 m per second from rest. What that means is that we have an initial velocity that zero, but our final velocity is 30 and then we've got this six seconds over here. That's a time so that's Delta T. What we're gonna do is we're going to calculate the magnitude of the Applied Force that's pushing the block. This is a forces problem. So the way we saw forces problems is first, we have to draw a free body diagram. Let's go ahead and do that. So we're gonna draw a free body diagram like this. This is a friction surface, and the first thing we have to do is check for any weight force, right? There's always a weight force unless we're told that there is no way to force. So there's a wait right here. Then we look for any applied or tension forces. Remember that this block is being pushed, so you can just assume that that is an applied force like this. So that's my F A. There's no cables or tension or ropes or anything like that. So there's no tension And the next thing we look for is if two surfaces are in contact, well, there are because there's this block is on some surface like this. So there's a normal force. That's the reaction to the surface push, and then we check for any friction. Last, remember, this is this is a frictionless surface, so there is no friction or anything like that. So this is the free body diagram. So the second step is now we're just gonna write f equals ma. So I'm gonna go ahead and do that. So I've got f equals m a over here, the net force. Now, in this particular case here, we're calculating the magnitude of the Applied Force. So we're really looking for is looking for F A. Because this is the only force that's actually pushing this block to the rights. And that's the only force that we're gonna look at in our F equals ma equation. So you've got f a e equals m a over here. So to solve this, I need the mass and the acceleration, so we've got f A equals. Then I've got this is 20. That's the mass, and then the acceleration, the problem is that I actually don't know what that acceleration is. I don't know what this a variable is so I needed in order to solve for my applied force. So if I can solve for this A, then I can figure out my f my applied force. So how do I figure out this acceleration? Remember that we said here was that acceleration was the shared variable between these two sets of variables. It's an F equals m A. But it's also inside of all my motion equations and my motion variables so I can use as I can use one of these motion equations to solve the acceleration. So really, just gonna use the same process that we've used before. So I need three out of five variables I've got my Veena Devi Final, Delta X and Delta T. So what happens is I've got three of those five variables here, and I can just pick one equation that's going to give me my acceleration. So really, what happens here is that this acceleration variable a is the link between your force and your motion problems. If you ever get stuck using F equals m a, then you can always use your, um, equations to solve and also vice versa. If you get stuck using, um, equations, you can use ethical dilemma. So I've got here is I've got 3 to 5 variables, which means I can pick one of my five equations or four equations. That's gonna be the first one, Which is that v Not there. Sorry. The final equals V initial plus a times t. So I've got my V Finals 30 my Vienna zero. Then I've got a times six. And if you go ahead and work this out, you're gonna get 30/6, which equals the acceleration, which is five. So now we can do is just plug this variable back inside of this equation over here. So I've got my applied force is 20 times five, and my f A is equal to 100 Newtons. And that's the answer. There's 100 Newton force that's pushing the bloc, causing it to accelerate. That's it for this one. Guys, let me know if you have any questions.