Forces & Kinematics

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.

All right, guys, let's check out this next one. Here we have a 1000 kg rocket that is accelerating upwards due to some thrust. So I got this rocket like this. I know the mass is 1000, and I got a couple of forces on it during the 1st 20 seconds of its motion. We know the Weight force or the force of gravity downwards. This is my W is going to equal 10,000. We also have a couple of other forces, like the force of thrust that's basically like an applied force. So what I'm gonna do is I'm gonna call this F T for thrust. I also have a force of air resistance that's acting downwards because this rocket is going to start accelerating. We're going to start moving upwards like this. So what happens is the air resistance I'm gonna call this F air is gonna point downwards. And I know this is 5000. I also know this thrust is 25,000. Alright, So I've got all these forces. There's no normals or frictions or anything like that. What I want to do is figure out the rocket's velocity after 20 seconds we know that the initial velocity is going to be zero because it's gonna start from rest. But then later on, it's gonna have some final velocity. So this final velocity is actually what I'm looking for here. So if I want to figure out the final, I'm gonna have to list out all of my other telematics variables, right? Like my initial velocity I want also want the Delta y. And then I had the acceleration end times I'll need all of these things. So the Delta y I don't know what that is. I know that Vienna zero starts from rest. The acceleration. I don't know either. And I also I know the time is 20 seconds. Right, So this is gonna be my 20 seconds here. So we have here that the two out of five variables, right? We have two out of five, which means we can't actually use an equation to solve for the final Yet we're gonna need another one of our variables, just like we have have done before. When we get stuck, we're gonna try to use this. Uh, we're gonna try to figure out this A by using f equals M a. So we're gonna use f equals m A to figure out acceleration. And we're now we're just going to add all of our forces in the vertical direction, right? All of our forces act only along the y axis. So what happens is this rocket is traveling upwards, so I'm just gonna choose the upwards direction to be positive. And so that means that our f t is positive and we expanded our some F and then our f air is gonna be downward, so it gets a negative, and then our weight forces also gonna be negative as well. So this equals mass times acceleration. Remember, I want to figure out this a here so I can plug it back into this, um, into my kinetics variables and then pick an equation. All right, so now I just replace all the values that I know. This is 25,000, then I've got this F air is 5000, and then I've got minus this 10,000 from the weight, and this equals mass, which is 1000 times acceleration. All right, so if you work, all this out you're gonna get is 10,000, you're gonna get 10,000 over here is equal to 1000 times a So that just means that our acceleration is 10 m per second squared. Alright, so our acceleration is 10, which means we now have enough information to figure out economics equation. Right? So now we have 3 to 5, and now we're gonna go ahead and just pick out one of the arrow equations. So I'm gonna go over here if I want to find out the final velocity. The final velocity is basically going to be the equation that ignores my Delta X right. So I'm gonna I'm gonna ignore my Delta X or my delta y over here, And that's just gonna be equation number one. So I got an equation number one, which is the final equals V initial plus 80. So I don't want the final. This is just gonna be zero plus now I've got an acceleration of 10, and then I got in a time of 20 so this is basically just going to be 200 m per second. All right? So look to your answer choices and it's answer choice A. That's it for this one, guys