00:01
So in this problem we have our pulley system, two of the pulleys are attached, the pulley in the middle is not, but we're working out when it is not moving, so we're going to consider it being stationary for working out.
00:14
Now we have two masses at the end, m1 which is four kilograms, m2 which is six kilograms, and our unknown m3 attached to the middle.
00:26
Now the kind of trick to this problem is that m1 and m2 are not the same.
00:33
Now if we imagine they just attach to one pulley, well obviously m2 would fall down more, right? and that's the same situation we have here because whatever m3 is holding this tension, holding this pulley in the same one spot, the tension of the rope is just going to go through and m2 is going to keep falling.
00:51
So we need to figure out the motion of m1 and m2 and then work out m3.
00:57
Another thing we need to look at is that the tension in the rope is all constant, so the tension at every part of the rope is constant, and depending on how we look at it, depending on which object we're looking at, picks the direction, the tension is all the same.
01:15
So we have one tension through the entire problem.
01:18
So let's look at the free body diagrams for mass 1 and mass 2, and we're also using here that exertion into gravity is 10 meters per second squared, so make the numbers round.
01:31
So for mass 1, we have its weight which is mass times gravity, four kilograms times 10, 40 newtons, then a tension upwards here, and our axis x and y.
01:49
Now for mass 2, it has a weight equal to 60 kilograms, or a weight equal to 60 newtons, of course a mass of 6 kilograms, and the same tension t upwards, and t is going to have of course the same value on both of these equations.
02:04
Now what we were talking about before is that the acceleration on block 2 is going to be downwards because it's the heavier mass that's going to fall more, because the force it creates is larger.
02:15
So that's the acceleration downwards, and the motion of the rope, because it doesn't stretch, is all the same.
02:20
So if the rope is going downwards here, it travels upwards here, downwards here, upwards here.
02:26
So mass 1 is accelerating upwards.
02:30
So let's make our axis so that all the accelerations are both in the positive direction, makes life easy, so we have x and y like this.
02:37
Now we can look at solving these.
02:42
We have all our forces in the y, and so newton's second law, sum of forces, only need to consider the y -axis is equal to ma, because of course these are moving.
02:54
So the tension minus the weight is equal to the mass of block 1 here, 4 kilograms, times acceleration...