6. Intro to Forces (Dynamics)

Vertical Equilibrium & The Normal Force

# Multiple Cables on a Loudspeaker

Patrick Ford

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Hey, guys, let's check out this problem here. We got this loudspeaker that's held in place by four vertical cables. We know the tension in each cables. 30. So, basically, I'm gonna draw this out real quick. Right? So we have this loudspeaker like this, I don't know what the masses, but I do know it's held in place not by one cable, but actually by four. And I know the tension. Each one of these cables is 30. What I want to do this problem is I want to figure out the mass of this loudspeaker. So I actually want to figure out what is this M here? All right, So what I wanna do is I want to draw a free body diagram because they've had some tensions that I've got, you know, things like that. So I want to draw a free body diagram first. So I got I got like this, remember, I have the weight force that acts down. This is gonna be my mg. This is my target variable here. And then if there are only one cable that was attached to this, I would draw one era like this, right? There's actually four So what I need to do is I need to draw four identical arrows like this, and these are all going to be the tensions. These are all supposed to be the same size. So each one of these tensions here is 30. So if I only had one would be t equals 30. But I basically have to account for all four of these tensions. And I don't have to write it all four times, right, cause I know each one of them is 30. All right, now I've got no applied forces normals or friction or anything like that. I'm not directly pushing or pulling it, and it's also not in contact with anything, right? So those are the only two forces. So now I want to draw. I want to write out my f equals M a. Right. That's how we how we solve problems. So we have our f equals m a here. So the sum of all forces equals mass times acceleration. We just choose our upward direction to be positive. Now we're just gonna expand our EFS. There's a couple ways to do this, right. We have actually four tensions that point upwards, so one way you can do this, you could have tension plus tension plus bah blah. But that kind of gets annoying. So instead what you can do you say? Well, if all these tensions are the same then we're just four times t right, four times the same tension. They're all the same value and then we got mg downwards. So this is minus mg equals m A. All right, so we're trying to find this mass here. I know the tension. So I also know the G. The only other variable I don't know is the acceleration. What is the acceleration of this loudspeaker that's being held by these cables? So here's what we do. You have to go back to the problem and see if we can figure it out. What this problem tells us, though, is that this loudspeaker is held in place by these cables. So what that means is that the velocity is equal to zero and it's held in place. It's not going anywhere, and it's also going to stay that way, which means that the acceleration is equal to zero. There's gonna be no change in velocity. Alright, so we can do is we're gonna imply and infer from the problem. You're supposed to figure it out that this acceleration is equal to zero. And so this loudspeakers at equilibrium. So that means we can just set four t minus mg equal to zero. And now you can set up our equation and solve for M. So basically, when we move m g to the other side, we're gonna get 40 equals mg. And now we just divide this G over to the other side. So really are m becomes four times the tension divided by G, which is four times 30 divided by 98 You work this out, you're gonna get 12.12 kg. So you look for your answer choices and that's answer choice. Be alright. So each one of these tensions here is 30 Newton's. But all of them together add up to 1 20. This kind of makes some sense. If there was only one cable, it has to have to support the entire weight. If there are two cables, they could kind of split it evenly. There are three cables that could split the way distribute among the three cables. If there's four and so on and so forth. You get the picture. So that's why each one of these tables these cables here doesn't have to support damage. Wait. All right, That's it. That one.

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