 After you have practiced doing dynamics problems with one object you can book how to solve problems with two objects or even more. I have the same procedure as I have for one object. That is, first step is to find the free body diagram. Then select the coordinate system, then write down the formulas you're going to be using. Then look at the components, fifth solve it and then the uncheck it. The main difference is that instead of having one free body diagram, we now have more than one free body diagram. We have one free body diagram per object. The problem I want to be looking at is we have that box that is on wheels. We're going to assume no friction. There is a cable that goes over an ideal pulley also with no friction and no inertia. Then there is a weight that is suspended on the other side of the cable. We want to figure out what's the acceleration of the cart and what's the tension in the cable. Free body diagram. Let's draw the one of mass one on the left side and the one of mass two on the right side. Then we do it the same way as we did before. So I'm going to isolate my cart. I'm going to have something here. That means I'm going to have a force that goes to the right on this one. I have a force here from the surface and we have no friction so that's only the normal force. So this is the normal force on block one. Then we have force of gravity on one. And this one here wants the tension on one by two. On one by two. And then I will have my acceleration to the right. So I'm assuming the thing has acceleration A1 to the right. For my second object I'm going to be circling here. So I have to cut something here so I must have a force that goes up. Which is a tension on two by one and nothing else except gravity. And if this one is moving to the right then of course that one here has to accelerate downwards. So A2 goes that way. And I have my everybody diagrams. Next step, select the coordinate system. So why not use the regular coordinate system here? X, Y, and why not use the regular coordinate system here? Now step number three, the formulas I'm going to be using. Well here I have gravity. So I have F, G1 is M1 times G. Same thing is right here. So F, G2 is M2 times G. Then if there is a cable that has no slack and that's not flexible. That means if this one moves a bit this one has to move the same amount. So the two accelerations must be the same. So A1 is equal to A2. And let's just call this A as acceleration. Also new we have need the third option. If object 1 is pulling an object 2 then object 2 is pulling an object 1 with the same magnitude in opposite direction. So T12 is equal to T21. Let's just call this one T. And you can check opposite directions. Yes, this one is pulling this way on the cable, the other one is pulling that way on the cable. And what else do we have? Of course we have the second one. We are going to have some of all forces is an A. And we are going to have here in Y direction. We are going to have some of all forces is 0. And the acceleration is 0. So next step called components. Let's start with the easier one. That one here. There is nothing in X direction going on. So all I have is Y direction. Which law do I have in Y direction? I have Newton's second law in Y direction. Some of the forces are my or my A. When we look at my forces I have my attention to 1 FG2 and to A2. If I look at the signs, my attention is in positive direction. And I say that can be replaced by just T. And then I have my FG which is in minus direction minus M2G. And then I have my acceleration. My interest in heat acceleration goes in negative direction. So for once I have a negative here and to A. So this is my first equation with two unknowns. So I cannot solve it yet. But I have one equation with two arms. If I look at my object 1. I am having a next direction and the Y direction. In my direction I don't have an acceleration. So here we have Newton's first law. And in the next direction I have my acceleration. So Newton's second law. So my forces, the normal force goes in Y. Gravity goes in Y plus FG and so on. And my tension, tension 1, 2 is mass 1 A1. So if I plug in my magnitude's tension is mass 1A. Now this one here doesn't give me anything. If I am looking for the tension or the acceleration all this one is going to give me that in this case the normal force is equal to gravity. But I don't need to continue here. This is my second equation. My unknowns, my unknowns are the acceleration. And T is the two unknowns, two equations. Therefore Amath teacher will tell you this system of equations is solvable. So let's try with plugging in T into that equation. So let's put 2 in 1. I am replacing the T here with my M1 alpha. So I have M1 acceleration minus M2 G. This minus M2 acceleration. I have one equation and that I should be able to solve for the acceleration. So what can I do? Everything in the explanation has to be on one side. M1A plus M2A is M2G. So I have acceleration is M2G over M1 plus M2. I am actually not going to solve it with numbers. I am going to leave it in symbols here. And then I can replace this with my equation 2. So tension is mass1 times mass2 times G over mass1 plus mass2. So last step, check it, does it make sense? So if I look at my acceleration, my acceleration increases the more mass I am having here. Do you think whether that makes sense? The more mass I have, this is the driving force. This is what accelerates my system. So that seems to make sense, depends on the gravitational constant and then divide it by the total mass of the system. This is the inertia of the system, the total inertia that I need to accelerate. This is the bigger inertia, the lower acceleration. So this one seems to make sense. So I would say must be correct. And then the tension is simply the acceleration times mass1. So it looks like in the end, once I have the acceleration, I simply have to multiply it by that mass and then I find the tension here. And it looks to me like that's tensile as well. So I would say I checked it. And I went through all the steps. And I think my problem is solved. Now all I have to do is plug in the numbers and I have the answers.