00:01
We're going to draw our image here just to kind of see our situation before we do our diagram.
00:08
So we have this uniform board, and it tells us it is two meters long.
00:14
So the whole thing is two meters.
00:16
And since it is uniform, the mass of the board, when we're doing our diagrams, we're going to put it at the center.
00:22
This is the center of mass.
00:23
And it tells us it is 71 kilograms.
00:26
So that's 71 kilograms going down.
00:28
So our force of gravity is 71 times gravity, which is 9 .81.
00:35
If you use 10 in your class, go ahead and put 10 in that place.
00:39
So force of gravity, remember, is just mass times gravity.
00:41
I'll put that here so you can see it while we're doing it.
00:44
We're told that two people are holding up this board.
00:47
One person at the very end, and his name is will.
00:50
So will is holding it right here.
00:52
So the upward force would be the force.
00:54
I'm going to put up w of will.
00:56
And then the other person is right here.
01:00
Is not holding at the edge.
01:02
He's holding it a little closer.
01:04
So he's going to have an upward force.
01:05
I'm going to call that force of cliff or force of c.
01:09
And he's about 0 .6 meters from the end.
01:16
He is not at the end.
01:18
But at the very end, we're going to have his lunchbox, which is 200 newtons, hanging from it.
01:25
So the first thing we need to do is draw an extended free body diagram.
01:29
So we're going to draw this a little neater, but in a free body diagram in green.
01:33
So here's my board.
01:39
Here's my center of mass.
01:41
So we know going down is our force of gravity.
01:45
And if you want to include the value in that by mass times gravity, if you use 10, it's 710.
01:51
But if you use the standard 9 .81, it is 696 .51.
02:00
You also have at the very end, let me draw that a little shorter in case you're doing this to scale of 200 newtons, and this is the lunch.
02:17
And then you're going to have will at the end.
02:19
We don't know how much these are doing yet, so we're not quite sure yet how to draw our diagrams.
02:25
And then about right here, we have force of cliff.
02:28
And you can actually kind of tell that cliff will be doing more of the work because he has the lunch next to him.
02:33
So i'll go ahead and shorten that too.
02:35
Here's a little cleaner looking free body diagram.
02:38
Now we need to find the force that both cliff and will provide.
02:45
And so to do that, we're going to look at our two conditions of equilibrium.
02:49
So the first condition, force net equals zero.
02:53
If it's at completely equilibrium, all the forces will cancel out.
02:57
And so that means all our upward forces minus the downward forces.
03:02
We're going to take down as negative equals zero.
03:05
So that means our upward forces must equal our downward forces.
03:09
They are canceling out.
03:12
So let's look at all our upward forces.
03:14
Well, we have will and cliff.
03:17
So our up forces are the force of will plus the force of cliff.
03:22
And they're equal our downward forces, which is the 696 .51 plus the 200.
03:29
Now, if you're wondering why i didn't put this as negative, i've already taken care of that here.
03:34
That's why that downward was negative.
03:37
All right.
03:38
So so what's going to happen here is that we're going to have two unknowns.
03:44
Well, we can't solve this here.
03:46
We know that the two forces of the men together will equal about 900, but we don't have that yet...