00:01
So this is a question that they want us to solve using the conservation of energy.
00:07
Here is a situation.
00:09
We have a table here and on this table we have a block which they've labeled block one and block one is connected by a massless rope over a massless and frictionless pulley to block two and block two is free to move down and when it does block one will move to the right.
00:35
We're going to take as our system the gravity of the earth and the two blocks.
00:43
So what we need to do is consider are there any outside forces acting on our system that are going to take energy away or add energy to our system via work.
00:53
Well the only external force acting on block one since gravity is a part of the system is the normal force acting up from the table.
01:05
But that normal force is acting perpendicular to the motion of block one so that normal force will not do work on our system.
01:16
Similarly the only force acting on block two that's from is the force of gravity and of course the tension with the tension of the rope is part of our system though.
01:25
But gravity is part of our system as well so that is not an external force so that is not going to change the energy of our system.
01:33
So the conservation of energy says that energy is neither created nor destroyed which means that because there's no external force doing work on our system the energy of our system should stay constant.
01:49
And because there's no non -conservative forces acting we're told this is a frictionless pulley and a frictionless table the energy being constant means that the mechanical energy will remain constant.
02:01
So all we need to do is set up an equation that shows the mechanical energy at the beginning of the motion and the mechanical energy at the end and set those two equal to each other and we should be able to solve for the speed of the blocks after block two falls.
02:16
Let's call little h the distance that block two falls here and let's call big h the height of the table that's the height that block one is at.
02:28
We can say that the energy before the blocks start to move is going to be the mass of block one times g times big h.
02:46
We call this big h here.
02:48
That's the height of block one is above our reference level plus m two times g times little h that's the height that block two is above our reference level at the beginning and there's no kinetic energy any other kind of energy act present here...