00:01
Chapter 9, problem 13.
00:06
Find the tension in the two wires supporting the traffic light shown in figure, 9 -53.
00:13
So here's our figure, 53 degrees off the horizontal.
00:18
In the left, 37 on the right of the junction that holds up the light and the lightways.
00:26
Well, the stoplight's mass is 33 kilograms, and it will feel a weight of that multiplied by g.
00:36
So the goal is to find basically the tension, t1 and t2.
00:40
So you can name those either way, t1 and t2, whichever you prefer.
00:48
But this can be a very simple problem depending on where we choose our center of mass, let's say, should be.
01:02
You might be tempted to look at the light as the point of mass, but then you would have to only include the tension, and it would just be a point mass like this, a tension like this, and mg, and this is just not enough information, right? we want to have both, we want to have both these tensions.
01:25
We don't only care about x, right? the general form of what we want to do is going to be put the center of mass here where this dot is so that we could have a free body diagram with simply t1, t2, and m g and then when we have this what we can do since we know some quantities we can start to break t1 into components and break t2 into components x and y components so it'll be x and this will be y right so both y are positive but the x's flip across the x axis well the x's the tensions flip across the x axis but this allows us essentially to add up the forces and we can use the equilibrium condition also to our advantage.
02:30
That when we talk about the sum of the forces, newton's second law says that this is equal to ma, but since the traffic light is not moving, this is equal to zero.
02:41
So this allows us to, oh yeah, like i said, you want to draw a free body diagram similar to what i had before.
02:47
And i just call the angles different names instead of the numbers.
02:52
So i could write them less.
02:55
But you should always remember that here, theta, on the left, the left angle is 53, and then the right angle is 37.
03:04
But yeah, so similar angles tells me that the triangle, if you look at the two horizontal lines, one right here and one right here, the angle is going to be the same.
03:16
This angle is going to be the same.
03:19
That is just a geometric rule that you should know.
03:22
But the same goes for the other side here and here.
03:30
But yeah, that helps us to make this triangle.
03:37
And once you've made this triangle, then you can really split up the components like we have here with cosines and signs and then start to do some calculations.
03:51
So some of the forces here we can sum the forces in the x direction.
03:56
And it turns out that the only two that we see are the t1x component and the t2x component.
04:02
In here, right? so they don't quite cancel each other out because they have different values, but they do equal each other...