00:01
So in this problem, it said that there was some ring with three forces, three strings tied to it unless there is three tensions.
00:08
If we look at the diagram and we put them all tail to tail instead of tip to tail, we would have vector a, vector b, and then basically straight downwards vector c.
00:21
And the magnitudes aren't to scale here, but just the directions.
00:25
Now we're told this ring did not move.
00:27
So we have forces, how we can relate that to movement with newton's segment law, where the magnitudes.
00:33
The sum of forces is equal to m .a.
00:36
Now this is strictly a vector equation.
00:39
Now if it didn't move, then that means that its velocity was equal to zero and it was constant.
00:47
And therefore, the acceleration should be equal to zero if the velocity is not changing with time.
00:52
So if the acceleration is equal to zero, then the sum of forces is equal to zero.
00:58
So you usually do this mathematically, but you could also look at this graphically, right? the sum of these forces, a, b, and c, should be equal to zero if this ring was not moving.
01:08
The forces are vectors, and so the sum of the vectors should be equal to zero, which means if we place them tip to tail, they should start and end at the same point.
01:16
Because the resultant is, of course, if we have two vectors, a and b, the resultant, a plus b, starts at the tip of a and goes to the tail of a to tip of b.
01:31
So in this problem, we have our three vectors.
01:36
And i'm not going to draw most of this to scale.
01:40
But what we care about just as this last part, we have vector a, vector b, and c.
01:46
So vector a starts at the origin, 0 ,0, in our x, y space.
01:52
And we know that each grid space here is a newton.
01:57
And so we see vector c ends this at negative 1 and 2 newtons.
02:08
So what is the error then? well, we expect this to be coming to the origin, but it's not...