00:06
Problem 4 .86 is a 3 -force rigid body problem, where we have the force of the weight of the rod, as well as the forces in these two cables.
00:26
So the tension coming from b and the tension in the cable from c.
00:39
Now, since this is a three -force body, all three forces are concurrent, which means their line of actions meet at the same point.
00:47
And the first part of this problem asks to find the angle theta.
01:06
To do that, we're going to have to do a little geometry.
01:10
So i'm going to make a right triangle here and label the points e and f.
01:21
And using the sign of 40 degrees, we can find the length ef, which you will need to find the angle theta.
01:34
Ef is the opposite side, and the hypotenuse is one -half the length.
01:42
Because the weight of the rod is assumed to be in the center.
01:53
We get that it's .321l.
02:01
Now if i draw out the triangle between e, c, and f, we can find this angle theta.
02:21
This angle of the triangle is going to be 90 minus theta because it is perpendicular with the horizontal.
02:31
We just solve for this length, 0 .321l...