00:01
So in this problem we have our beam, which is in three dimensions here, and we have our two forces f a, which is, i can draw the angle correctly, we have our 3 4 here and f a is 1000 pound force.
00:20
And then f b, we have 1 1.
00:25
So these are, these forces are in the z, the y z plane, and then we have x out in the beam.
00:33
And our top force here is 600 pound force.
00:42
We have four inches to the first one and another six inches to the second one.
00:50
And then along our beam, we're going to have reactions in the y and z.
01:03
Now, so we are going to assume them to be in the positive direction.
01:06
So some reaction in the y, some reaction in the z.
01:14
And then looking at moments, moments follow the right hand rule.
01:19
So if we take our thumb, point it in the direction of the positive axis, rotate our fingers around it with our right hand, which is really important, that gives us a direction that the positive moment rotates.
01:30
So we have a moment in the y, m y and m z.
01:42
So looking at reactions first, this beam is in equilibrium.
01:46
So sum of forces by newton's second law is equal to zero.
01:50
Let's look at the y first.
01:51
Well, we have r y and then we have y components of the two forces.
01:58
Now they're both downwards.
02:03
And looking at the angles, we are given the rise and run.
02:07
So the whole component is based on the whole, we have the whole hypotenuse and then the component in the direction that we want.
02:14
Now, 3, 4, 5 is our triangle here by pythagorean theorem.
02:18
The two components are mutually perpendicular and it works out that 5 squared is equal to 3 squared plus 4 squared when we take the square root.
02:26
Now the 1, 1 here, we have our hypotenuse is the square root of 1 plus 1, which is just root 2.
02:35
So a little less convenient than just the 5.
02:39
So sum of forces in the y.
02:41
We have our 1000 pound force.
02:44
Now that component we see is downwards in this direction.
02:49
So it's negative 1000 pounds.
02:53
But we want the four fifths component because that's the number that is with our direction and then the total angle or the total length.
03:06
Now, same thing for the 600 pound force.
03:11
It's bulk downwards in the y direction and then 1 over root 2, 600 pounds.
03:21
I guess all of the 600s are actually 600 over 2 because the 1, 1 means both directions have the same component.
03:29
Now this is equal to 0.
03:30
So we just move the other components over to get our y to be 1224 pound feet.
03:38
Now doing the same thing in the z direction, sum of forces in the z is equal to 0.
03:46
Rz in the positive.
03:51
And then we have our 1000 in the negative direction, our 600 in the positive direction.
03:55
And then we're using the other component because we are looking at the other axis.
04:02
So minus three fifths, 1000 plus 600 over root 2.
04:11
I'm going to leave out the 1 because, well, it's just 1.
04:13
And this is equal to 0...