00:01
Here we have a static equilibrium problem, and so we need to start thinking with a free body diagram.
00:07
So we can take our body free from the external reactions and replace those reactions with the forces.
00:13
So we have a, b, c, that is c, and this is d.
00:21
We have our applied loaded d, which is equal to 100 kilograms times g.
00:26
The acceleration to grab down that gives us the weight.
00:28
Now at point b we have a roller, which means we can only exist a vertical load, and we'll use a normal reaction, so this is going to be b of y.
00:40
And at a, we have a pin, which can resist no moment, but forces in both directions.
00:46
So we have an ay and an ax.
00:51
So we need to pick an axis, and we've already shown which direction it is.
00:55
We'll pick x and y.
00:56
We'll put the origin at a, and that's going to be helpful in part a, to find the external reactions.
01:07
So what we want to do then is look at, well we have part a, just the first part, find the external reactions.
01:16
And so if the body is in static equilibrium, that means forces as well as moments, summed up equals zero on the body.
01:24
We take positive to be counterclockwise.
01:26
Now let's take them about point a.
01:28
We know that a moment is a force times a distance, if those are perpendicular, distance goes to zero, so does moment.
01:36
So the forces at a make no moment about a because they go directly through that point.
01:40
So the only unknown we have in the moment equation about a is b .y.
01:45
So that's good.
01:46
We have one equation and one unknown we can solve for.
01:48
If we see b .y, that tends to rotate about a clockwise, a counterclockwise direction.
01:53
So it's a positive moment, whereas our 100d is a negative moment.
01:58
And the distances we have are three meters, and then we have three meters across here, and and 4 meters across to point d.
02:15
And so if you look at the moment of b .y, we don't know what its force is.
02:20
We said it makes a positive moment, though, but the distance is 3 meters based on the diagram.
02:27
And the weight at point d was a negative moment.
02:30
Excerction to gravity 9 .81 meters per second, and the distance is 3 plus 4 or 7 meters, and this is all equal to 0.
02:40
So pretty easy algebra.
02:42
Move term over, divide by 3, and we see b y is 2 ,289 newton.
02:51
So now we can go back to sum of forces and see sum of forces in the y is equal to 0.
02:57
So we have a y, and we assume these unknowns in the positive direction just makes it simple.
03:01
If the answer is positive, it's in the positive direction.
03:03
If the answer is negative, it's in the negative...