Lowering a Load of Bricks

by Patrick Ford
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Hey, guys, let's check out this problem. We've got 100 kg load of bricks that's being lowered on a cable. So basically, I've got this load of bricks that's 100 kg just gonna draw as a box. It's being suspended by a cable, But that cable is actually lowering This load of bricks into the velocity here is equal to 5 m per second and eventually what happens is over some period of two seconds, it's going to slow to a stop, which means that there are some time period here. I'm gonna call this tea, which equals two seconds. Eventually, this load of bricks will come to a stop, which means the velocity is going to equal zero. So I'm gonna do is I'm gonna call this the initial velocity, which is my 5 m per second Final velocity is zero. What I want to do is I want to figure out what is the tension in the cable so that this, uh, this load of bricks actually comes to a stop. Right? So the first we have to do is going to draw a free body diagram. So I'm gonna do that over here is gonna be my free body diagram. So basically, I'm gonna have this little dot like this. I have the weight force. The weight force is going to be downwards. This is my w equals mg. And that also got attention force like this. And this is basically what I'm trying to solve for All right, So if I'm basically trying to solve for this tension force again, we look at any other forces. There's no applied forces because I don't have anything pushing or pulling. You also have a normal or friction because this thing is in the air. Right? So our free body diagram is pretty straightforward. Only these two forces and now we're going to f r f equals M A. So if our ethical dilemma we have to expand our forces, we need to know the direction of positive. So we're just going to choose the upward direction to be positive. All right, so now we've got our forces. We've got tension that's upwards. And then RMG is downwards, so our equation becomes t minus. MG equals m a. Now we want to figure out what this tension is, so I need to figure out everything else in the problem. I have to know mass. I have to know G have to know mass and the acceleration. But do we actually know the acceleration? We actually don't If you look at the problem, all we're told is that this thing is going downwards at 5 m per second and then over two seconds, it stops. That doesn't tell us what the acceleration is, and so we're kind of stuck here. How do we figure this out if we don't know the acceleration? Well, remember, what happens is that if you ever get stuck solving for a, you can always try to solve it using a motion equation. And that's exactly what I'm gonna do here. So if you want to figure out the acceleration, I'm gonna need to write out my five cinematics variables, right? I'm giving stuff like initial velocity, final velocity time. So these are all motion variables. So I need to know the Delta y this is my V, not V a n t. So I just need to know three out of five variables and then I can pick an equation to solve. So I don't know what my delta Y is. I don't know the distance that this thing is stopping through. But I do know my initial velocity is five. Is it five, though, or is it negative? Five. Remember, what happens is that the direction of velocities and accelerations depend on which direction you choose to be positive. We chose up to be positive. So this V not actually points down, even though we write it as a positive in the diagram we're doing math. We actually have to write it with the correct sign. So it's negative. Five. The final velocity zero. The acceleration is actually what we're trying to find here, and we know the time is equal to two seconds. So fortunately, what happens is we know 3 to 5 variables 123 So we can just pick the equation that ignores my delta. Y right, I'm just gonna ignore that one. And that equation is going to be the simplest one Number one which says that the initial velocity Final velocity is going to be initial velocity plus a times T, so we can use this to find a. So our final velocity is zero initial velocity is negative. Five plus and then we got eight times two. So if you bring this negative five words to the other side, it becomes positive. So five equals two a and so your acceleration is going to be 2.5 m per second squared. So let's talk about the sign. Remember that when you saw for the acceleration, as long as you've plugged in everything correctly, you should get the correct sign and it should indicate that the accelerations direction so which means, which means that we've got a positive number. That just means that we got an upward acceleration. So the upward acceleration is 2.5. This should make some sense, right? So if the load of bricks is going downwards with 5 m per second in order for it to come to a stop, the acceleration has to point upwards. Right, So we got an acceleration of 2.5. Now, you can just plug this number back into our F equals m a and then solve the tension. So what happens is we're gonna move this mg to the other side. Intention becomes mg. Plus, you could also just move. You can merge this into under under parentheses. That's up to you. So the tension is equal to, and now we just plug everything in 100 times 9.8 plus 100 times the acceleration, which is 2.5. We plug it in as a positive, remember? So if you work this out, you're gonna get is 1230 Newton's. So we look to our answer choices 12. 30 and that's going to be answered. Choice A. So we've got our attention is 12. 30. This should make some sense that we got a 12 30. Because in order for the acceleration to be up right, which to which we want for the load of bricks to slow to a stop, it has to be bigger than your weight force, which is 980. So even though the load of bricks is moving downwards, the tension force still has to be bigger to produce an upward acceleration so that the load of bricks stops. All right, so that's if this one guys