00:02
So in this problem, we have a table, and on our table we have a 5 kilogram mass, and attached to that mass is a rope.
00:18
A rope goes to both sides, and on there is a pulley over here, and the hanging mass over here has a value of 2 kilograms, and the hanging mass has an unknown mass, which is m.
00:36
So we're also stated in this problem that the acceleration of our 5 kilogram mass is equal to 3 meters per second.
00:48
And so really quickly we want to define what is positive and what is negative.
00:53
So what i'm going to say is that the direction that is going counterclockwise is positive.
01:01
And so thus we can say that our acceleration of our 5 kilogram mass going to the left.
01:09
Now, the first part of our problem is asking us to draw and assess the free body diagram of the 2 kilogram mass, and so that's over on the right.
01:22
So if we draw the free body diagram, let's go ahead and draw this, we of course have the weight of our 2 kilogram mass, which i'll denote as w2, and that's equal to our mass, which is 2 kilograms times gravity 9 .81.
01:41
So we get that the weight is equal to 19 .62 units.
01:50
Now acting on this mass, this mass 2, we also have a force of tension, which i will denote as t2.
01:59
And t2 is something that is unknown at the moment, but we can still solve for it.
02:06
And so if we assess our free body diagram and performing the sum of forces on our mass 2, well, we know that our mass 2 is equal to 2 kilograms.
02:21
And so the net force acting on it because we have an acceleration that is defined for the entire system as 3 meters.
02:31
Oh, there should be meters per second squared.
02:33
Sorry about that.
02:34
And so we have an acceleration that is defined as 3 meters per second squared.
02:40
We can calculate the net force on our mass of 2 kilograms.
02:44
And so our net force is going to be equal to 6 newtons.
02:47
And by doing a 4 summation, we can say that t2 is pointing upwards, which we defined as positive.
02:55
And thus we can say that t2 minus 19 .62 is equal to 6 newtons.
03:04
And so now we can solve for t2.
03:08
Doing this, we get that t2 is equal to 25 .62 nivins.
03:15
And now we are asked to draw the free body diagram for our mass that is 5 kilograms.
03:27
So let's go ahead and do this.
03:30
And so now we have the mass 5.
03:33
It's 5 kilograms...