00:01
Hi there, so for this problem we have the situation that is shown in this figure.
00:06
We have two masses and the values for them, we're going to call this mass m1 and mass m2 so that the mass of m1 is 2 .2 kilograms and the mass of m2 is 3 .2 kilograms.
00:24
We are also told that both of these blobs are 1 .8 meters above the ground, and the pulley that is massless and frictionless, is 4 .8 meters above the ground.
00:47
So what we need to determine is the maximum height that the layer object reach after the system is released.
00:57
We're going to call that height h.
01:01
Now the first thing that we need to do is to draw all of the forces that are adding on these two blocks.
01:14
So we have the tension for both are the same because it is the same string and this string didn't stretch stretches and we also have the weight of the mass and and the weight of the mass m2.
01:35
So we are going to call this w1 and w2.
01:40
Now, since the mass m2 is heavier than the mass m1 or is massive, massive than the other one, and we know that then the acceleration for the mass m1 is going to be up or and the acceleration for mass m2 is going to be downward.
02:05
Now we said that we take the positive eruption in the direction of the acceleration for each block.
02:15
Now what we can do is apply newton's law to the forces that are acting on these two blocks.
02:23
Now since the only forces are all forces are acting on the white component we need to sum all of the forces in that component.
02:33
So we will have for the the mass m1, the sum of the forces is equal to the tension and it is positive because it is at the same direction of the acceleration minus the weight want and this should be equal to the mass m1 times the acceleration.
02:59
Now for the mass m2 we have something similar but in this case we will have that the weight is because it is pointing to the same direction of the acceleration.
03:13
So with that, and the tension is negative because it is pointed opposite to the direction of the acceleration.
03:21
So we said that minus tension.
03:23
And this is equal to the mass two times the acceleration.
03:29
Now with this, if we call this equation one and equation two, we can sum 1, weight 2, so that we obtain the following.
03:44
We can see that we can console the tensions, so we will have minus the weight 1 plus the weight 2, and for the other part of this equation, we have the mass m1 plus the mass m2 times the acceleration.
04:04
So we can obtain the acceleration from this expression.
04:08
So we obtain that the expression is equal to this weight.
04:13
We note that the weight is defined as the mass times the acceleration due to gravity.
04:18
So we will have minus the mass m1 plus the mass m2 for the weight 2 and all of these times g, this over the sum of the masses.
04:34
So we now what we need to do is to substitute all of these values.
04:39
So we note that the mass m1, the mass m1 is 2 .2 minus 2 .2 kilograms, plus the mass m2, which is 3 .2 kilograms.
05:08
And all of this, the sum of these masses, which is 3 .2 kilograms, plus 2 .2 kilograms, plus 2.
05:17
2 .2 kilograms.
05:22
And this times the acceleration due to gravity, which is 9 .8 meters per second square.
05:30
So plotting this information into the calculator, we obtained that the acceleration of this system is equal to 1 .81 meters per second...