Vertical Forces And Acceleration in the Y-axis

by Patrick Ford
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Hey, guys. So up until now we've seen lots of problems. We have forces in the vertical axis that cancel out, and therefore the object was at equilibrium. Well, you're gonna need to know how to solve problems where you have vertical forces that don't cancel. And so this actually gonna cause objects to accelerate in the Y axis. But really, we're just gonna 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 gonna get right to the example. So you've got a 5.1 kg block, it's in the air and we're pulling it using a vertical massless string. So 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 we have to do is we have to draw the free body diagram. So we've got a block like this, 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. This is gonna 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 pushing or pulling this thing. But we do have a tension force because we have some string that tension forces going to act upwards, right, because we're basically just hanging this block in 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 a 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 ethical dilemma, right? So we want to find the acceleration so we want f equals m A. And so there's really only two forces to consider our attention and our weight force. Remember, you just add the forces tension and weight, and that equals m A. And now we can just replace the values. So our attention is 70. Our weight forces negative 50. Don't forget that negative sign and this is equal to 5.1 times a So you got 20 equals 5.1 a. And so therefore, your acceleration is equal to 3.92 m per second squared. So we've got two things here. We know that this acceleration is not going to be zero, 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 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 that the acceleration is going to be upwards, and that's what that positive sign tells us. All right, let's move on to the next one here. So now we've got 30 Newtons instead of 70. But really, we're just gonna do the same exact thing. So we've got our box like this. We've gotta wait for us. We know that this is W. We know the Sequels to negative 50. And then we know that this tension force is actually now 30 instead of 17. We're gonna write a little bit smaller, that arrow. So here's the thing. So if we have a 30 Newton tension force we have what we have in part a is that if this 70 Newton force was bigger than our, uh, 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 wait for us. So we expect that the acceleration is gonna point downwards. Alright, so now we're just gonna do f equals m A. So we've got our attention. Plus our weight equals mass times acceleration. So now we've got our 30 plus negative 50 equals 5.1 a. And so this is negative. 20 equals 5.1 a. And so here the acceleration is negative. 3.92 m per second squared. This should make some sense, right? Because basically, now we know that the weight force was bigger or attention forced 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 forces still bigger than how hard you're pulling upwards. And so this blocks is still going to accelerate. Downwards. Alright, so now we've got here is we've got 50 Newtons and we're actually just gonna fill these out. We're gonna 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 that's negative. 50. But now what happens is we're pulling upwards with attention. Force of 50. So when you write out your ethical dilemma, we know that we have tension. Plus, weight equals Emma. So you've got 50 plus our negative 50 and that equals 5.1 a. So are 15 negative 50? Just cancel out to zero. And so what that means is that this block is in equilibrium because your upward forces and downward forces perfectly cancel each other out. So we know that the acceleration is equal to zero in this case because your forces are perfectly balanced. Remember, this is the equilibrium means Now, finally, we have attention of zero Newton's. That's not a typo. So here, what we've got is our block like this. And now we've got our weight force we know are w equals negative 50. But now we have our tension of zero which basically means that we don't even draw the tension force. Right? Really? The only forces acting on this thing is the weight force. So we do our f equals m A. And there's only one force acting on it. This time our weights equals m A. So we have negative m g equals m A. So negative 50 equals 5.1 a. And so you work this out and you're gonna get a is equal to negative 9.8 m per second squared. This shouldn't come as a surprise because if there's only force that's acting on, this is the weight force. Then we know from our video on the weight force that all objects are gonna accelerate downwards with an acceleration of negative G, which is negative 9.8. There's no other forces that are acting on this, right? So let's go ahead and summarize real quick if you're upward forces the magnitudes right? We're just thinking of the numbers Here are greater than your downward forces like we saw in this example. Here are 70 was bigger than our 50 downwards of weights. Then that means your acceleration is going to be positive, which means it points upwards now. In this case, when we had our upward forces less than our downward forces are, acceleration turned out to be negative, right? Basically, our weight forces in our downward forces were bigger or 50 was bigger than the 30. And so therefore the acceleration was downwards. And now if your upward forces perfectly equal your downward forces, then we know that to be equilibrium in your acceleration is equal to zero in this case. And then finally, if your upward forces are equal to zero, then that means that your acceleration is going to be exactly at negative G. Assuming that there's no other forces involved. Right? So that takes care of this video. Let me know if you have any questions.