00:01
So in this problem, we have two forces, and we will find the moment about point a, or the moment about the origin.
00:08
And we have two forces.
00:09
So instead of trying to do the moment equation twice, let's add the forces up, and then we can take the moment about them.
00:14
And this is fine because we can linearly add them.
00:17
And we have these two vectors.
00:19
So to add the forces, the sum of forces are which can call f with no subscript, we need to add the components.
00:25
So for force 1 was 100 newtons in the i, force 2, where we can call.
00:32
Was negative 200 newtons, or this actually pounds, pounds in the i -hat direction.
00:39
And we can do the same thing for j, negative 120, plus 250 in the j, and in the k, 75, and 150.
00:54
And so simplifying, and this whole thing would be pounds, i guess, we know what that's going to be, negative 100 i, minus 130.
01:08
J plus 175, and this is of course, pounds.
01:17
So we have that, and then we have our situation in 3d space, our pipe structure, and then we have the force.
01:30
If we know these axes are x, y, and z.
01:36
Force f, negative 100 to x, negative 100, negative 100, negative 130j.
01:41
So it is this way and this way, relative to x and y, and then going to be upwards.
01:50
So kind of hard to draw in 3d space, but our force would be something like this.
01:59
I guess you can represent it like that to kind of show the direction.
02:06
But it doesn't matter, though.
02:08
Then let's also look at the vector that is the radius from our origin, which is where we want to take moments to the force.
02:20
And this vector is going to be, well, the radius.
02:24
We get given the dimensions three feet up, four feet in the x and five feet in the y.
02:32
And so our radius vector is going to be directly.
02:38
Parallow to the x direction, we had four, so four i -hat.
02:41
Parallelow to the y, we had five, so five j -hat, and parallel to the z, three.
02:48
A 3 k hat.
02:51
Now we want these two vectors because we can find moment as a vector.
02:55
We know that moment is the cross product of the radius across the force, where the radius is any vector that goes to the intersection of the line of action of the force.
03:06
So here it's really easy just to go where the force is applied, and it's probably where you're doing most of the time.
03:10
Sometimes you can make this problem simpler.
03:14
And we have the cross product...