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ï»¿ Hello class. Professor Anderson here. Welcome to another edition of Learning Glass Lectures on Physics. Let's take a look at a tension problem and this was one that you guys recommended. And the problem looks like the following. We have a wall and a roof and we have a rope coming down right there. We have a rope coming here. They're all tied together in a ring and then there's a third rope coming down like that and we know a few things. There's tension 1. There's tension 2 and there's tension 3 and let's give you the tensions. T1 is 50 Newtons. T2 is 80 Newtons and we give you some lengths of these different segments so this is L1. This is L2. L1 is .8 meters. L2 is .6 meters and the question is what is T3? Okay, so the whole system is of course at rest and if we think about the tension T3 right, tension T3 has to counteract T1 and T2 but those are orthogonal to each other. They're at a right angle to each other and so the horizontal component here of T3 has to be what? Has to be exactly equal to T1 and the vertical component of T3 has to be what? Has to be exactly equal to T2. How do we see that? Well sum of the forces in the x direction. This is what we're calling T3x. This is T3y and if I think about the forces that are acting on my dot I have T1 going that way, T3x going that way. T2 going up. T3y going down. And so this is actually very straightforward right? T3x is going to the right. T1 is going to the left. That has to add up to zero if everything is at rest. So T3x is just T1. Sum of the forces in the y direction we have T2 going up. T3y going down that also has to add up to zero and so I get T3y is just equal to T2. What we're looking for is T3. T3 is the hypotenuse of this triangle. So Pythagoras tells us we've got to add up the X components squared, the Y components squared. Take the square root. But now we know exactly what those things are. It is the same as T1 squared plus T2 squared, square rooted. And we know those numbers. And if you plug them in, you get 94 newtons. It turns out we didn't even need the lengths here for this part, right? All you needed to know was the two tensions and that they made a right angle to each other. Alright. Not too bad. Questions about that one? Piece of cake? Good.

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