00:02
Alright, this question wants us to consider a traffic light suspended by two cables and find the tension in each cable because they're both hanging from the same angle of 20 degrees.
00:23
So, what we need to do is draw a free body diagram to find the forces.
00:29
So this is our traffic light, and we have its weight pulling down on it, and it says the traffic light weighs 12 pounds.
00:42
Then we have one tension force pulling it that way, and another tension force pulling it that way.
00:53
And it's said that both of these have an angle of 20 degrees.
01:00
So if the traffic light isn't moving, then f -net in the x direction has to be equal to zero, and f -net in the y -direction has to equal zero.
01:17
So if we look at our force diagram again, we see that in the y direction, we have the weight, plus the tension in the y direction from each pole.
01:41
And in the x direction, we just have the tension in the x direction from each.
01:50
So, since each pole is at the same angle, we know that all these forces are the same, which means the y component of 1 is equal to the y component of 2.
02:02
And same thing for the x component so y we have the weight plus two times the tension in the y direction then x we have two times the tension in the x direction because we're just going to call this tension force t so we'll solve for y first so we know that the f -net in the y direction equals 12 and that's a minus 12 because weight's pulling down and then plus two times our tension force so we know that the net force has to be equal to zero so we can solve so the tension in the y direction is 6 pounds.
03:10
So now we can update our diagram.
03:14
So this is 12.
03:21
This is 6.
03:28
And this is also 6.
03:32
So now we need to solve for the tensions in the x direction.
03:37
So we do that by using our newly found tension in the y along when we with our angle of 20 degrees...