And, I will, for assembling my equation, I'll assume up is positive. I could assume

down is positive. You may want to do that on, on your own to see that you get the

same answer. And so, first of all, I have a tension in cable OA. I have the y

component is the 5 side of the 5, 12th, 13th triangle. And so, by similar

triangles, that's going to be plus 5 13ths TOA, and it's positive because it's

pulling up. TOB does not have a y component. I have my 200 pound force,

which is down, so that's going to be minus 200. all in the y direction. And then, the

100 pound force, its y component is only the 4 5ths component. So, we have minus 4

5ths times 100 equals 0. And so, I can solve for TOA. TOA is equal to, it'll come

out to be 728 pounds. If I want to express it as a vector, I have to show the

direction as well. And so, it's going to be up and to the left on a 5 on 12 slope.

And so, that's my complete answer for TOA. So, I'm halfway there. And, you should ask

your, yourself, how can I find now the tension in OB? And what you should

determine is, well, I've used the equation for equilibrium in the y direction. Let's

try to use that other independent equation to see if we can find TOB or, and so if I

do that here is a sketch again of my free body diagram. And, here's my results from

the last slide where I summed forces in the y direction and found TOA was equal to

728. Now, let's sum forces in the x direction. I'll choose right as positive

for assembling my equation. And, first I have TOA. It's pulling to the left. Its x

component is the 12 13ths component of TOA, so that's minus 13 13ths TOA.

And then, I have TOB to the right, so that's positive according to my sign

convention. It's all in the right, all to the right, so it's just plus TOB. The 200

pound force does not have an x component, it's all in the y direction. And then,

finally, the 100 pound force has only the 3 5ths component in the x direction, and

it's going to be negative because it's pulling back to the left. So that's minus

3 5ths times 100 equals 0. So, I have one equation now, two unknowns.

But I've already solved for TOA. And so, I can substitute that in. That's 728.

And that'll allow us to get our final solution for TOB which is 732 pounds. And

again, if I want to express it as a vector, I should express it as a vector.

And so, I have to put a direction here, and so I'll call it to the right. And

that's my solution. That concludes today's module. Thank you.