Hey, guys. So up until now, we've seen lots of problems. We have forces in the vertical axis that canceled out, and therefore, the object was at equilibrium. Well, you're going to need to know how to solve problems where you have vertical forces that don't cancel, and so this is actually going to cause objects to accelerate in the y-axis. But, really, we're just going to use the same list of steps that we use for any forces problems to solve these kinds of problems. So this is really straightforward. We're just going to get right to the example. So you've got a 5.1 kilogram block. It's in the air, and we're pulling it using a vertical massless string. So what we want to do is we want to find the acceleration for each of the following varying tension forces. So we got the first one here, which is tension equals 70. So the first thing we have to do is we have to just draw the free body diagram. So we've got our block like this. And remember, we check for the weight force first. This is our weight force, and this is equal to negative mg because it's downward. Remember, up is positive, down is negative. So this is going to be negative 5.1 times 9.8 equals negative 50. So that's our weight force. And then there's no applied forces. Right? There's nothing nothing pushing or pulling this thing, but we do have a tension force because we have some string. That tension force is going to act upwards, right, because we're basically just hanging this block from the string. And so we know that this tension force is equal to 70, and it's upwards. So there's no contact forces. Right? There's no normal or friction because this thing is basically suspended in the air. So we just have the weight and the tension. So now we just go ahead and write s=ma. Right? So we want to find the acceleration. So we want s=ma. And so there's really only 2 forces to consider, our tension and our weight force. So remember, you just add the forces, tension and weight, and that equals ma. And now we can just replace the values. So our tension is 70. Our weight force is negative 50. Don't forget that negative sign. And this is equal to 5.1 times a. So you got 20 equals 5.1a. And so, therefore, your acceleration is equal to 3.92 meters per second squared. So we've got 2 things here. We know that this acceleration is not going to be 0, right, because the forces are not going to cancel. But the fact that we get a positive sign also means that we know the direction of this acceleration. So if this 70 newton tension force is greater than your 50 newton, force of gravity that acts downwards, If you think about this like a tug of war, then that means your tension force upwards is going to win. And so, therefore, you would expect the acceleration is going to be upwards, and that's what that positive sign tells us. Alright. Let's move on to the next one here. So now we've got 30 newtons instead of 70. But, really, we're just going to do the same exact thing. So we've got our box like this. We've got our weight force. We know that this is w. We know this equals to negative 50. And then we know that this tension force is actually now 30 instead of 70. So we're going to write a little bit smaller, the arrow. So here's the thing. So if we have a 30 newton tension force, what we have, what we had in part a is that if this 70 newton force was bigger than our, 50 newton force downwards, then we had an acceleration that was up. Well, here, we've got this 30 that's actually smaller than our downward weight force. So we'd expect that the acceleration is going to point downwards. Alright? So now we're just going to dof=ma. So we've got our tension plus our weight equals mass times acceleration. So now we've got our 30 plus negative fifty equals 5.1a and so this is negative twenty equals 5.1a. And so here, the acceleration is negative 3.92 meters per second squared. This should make some sense, right, because, basically, now we know that the weight force was bigger. Our tension force upwards was smaller than our weight force. And so here, what happens is you have an acceleration that points downwards. And so even though you're trying to pull this block up, the weight force is still bigger than how hard you're pulling upwards, and so this block is still going to accelerate downwards. Alright? So now, what we've got here is we've got 50 Newtons. And we're actually just going to fill these out. We're going to fill these out, in just a minute here. So we've got 50 Newtons. So we've got our block like this. We know our weight force. It was negative mg. We know this negative 50. But now what happens is we're pulling upw
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6. Intro to Forces (Dynamics)
Vertical Forces & Acceleration
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