00:06
Problem 4 .85 is a 3 -force rigid body problem.
00:12
Or we have two forces of the reaction forces at a and b.
00:17
The third force is the weight of the rod.
00:25
The weight is given as 8 kilograms, so to convert that to a force, multiply it by acceleration of gravity, 9 .81 meters per second squared, which gives us 78 .48 neutrons for the weight of the rod.
00:46
And since the slender collars on both sides are frictionless, it means that the only force is going to be normal to those slender collars.
01:00
So the reaction force at a goes horizontally, since the collar is vertical, and since it is a three -force rigid body where the lines of action of two forces meet, the third must also intersect there.
01:38
Now the first part of this problem asks for the angle of theta, we can find that since we know that beta is equal to 30 degrees given in the problem.
01:53
And we can find it making a few triangles.
01:56
So i make this point c where the lines of action intersect.
02:00
I make a right triangle here between b, c, and that intersection point.
02:07
I'll call that point d.
02:11
We can find the angle.
02:14
Because we know that this angle here is 30 degrees since the force acting from point b, the reaction force has to be perpendicular to the collar because it's the same as a beta.
02:41
We can set the tangent of that angle equal to its opposite side, cd over its adjacent side, bd.
02:55
And we can put cd and bd in terms of l and theta, so we can find theta...