Hello everyone and welcome to Jam Academy. In this example we have a man of Mars M1 standing on a platform of Mars M2. He pulls himself upwards using a row over a mass less and friction less pulley. So the question is we need to calculate the acceleration of the system. The force that he asserts on the platform that is a good one and the third question is what would be F for him to pull up the system at a constant speed? That is a great one. In other for us to do this problem which students often find it very difficult is just to draw the right free body diagram. For a matter of illustration I'm going to draw the free body diagram for the platform only, for the man only and for the man and the platform. Let me see that again. I'm going to draw the free body diagram taking the platform as our system only, taking the man as our system only as well as a combination of both the person and the platform as our system. So pay attention. The platform is two and the man is one according to the levels. So we know that the platform obviously has weight so there is a force of gravity that the earth asserts on the platform. This is M1D. Now there is also the normal force. Remember the guy is standing on a platform. So the platform asserts a normal force on him upwards by Newton's dead law. He also asserts a normal force on the platform downwards. So I'm going to denote that normal force here. So this is the normal force that the man asserts on the platform. Now if you look at it the platform is tied to a rope and he pulls the rope downwards and asserts a tension force upwards and that tension forces chance needed from where he pulls the rope onto the platform. So we have a tension force acting C. So if we want to translate our diagram it will look like this. You have tension upwards. You will have the normal force asserted by the man on the platform downwards and you will have the weight of the platform acting downwards. The system is accelerating upwards keep that in mind. So let's move on to the man. Obviously we have the weight of the guy acting downwards. This is M1G and we have the normal force that the platform asserts on him. Also remember the guy pulls the weight, the pulls the rope downwards. This is the point where students often missed it. He pulls the string downwards by Newton's third law the string will pull on him upwards. Now with an equal but opposite the directed force that means that we have a tension force acting on him upwards. So if we do the free body diagram we will have two forces upwards. There will be the tension and that will be the normal force 2.1 and we will have one force downwards which is M1G. So if we consider the guy and the platform as a system I'm going to do this. If we consider this as a system then you will notice that the weight of the system will act downwards. So the weight of the system will act downwards. This will be M1 plus M2G. That is the weight of the person and the weight of the platform altogether and the upward force acting on the system will be 2T. Look at it carefully. He asserts a downward force F and by Newton's third law the string asserts an upward force on him. By Newton's third law the string asserts an upward force on the platform. So if you put the guy and the platform together there will be two forces pointing upwards on all tension forces. So the very first question is for us to determine the acceleration of the system looking at our free body diagram. The question I want to ask is there are three free body diagrams right here. You have the free body diagram for the platform. This is M1 plus M2G and this is 2T. So the question is which free body diagram will help you the most? Which free body diagram will help you the most? Just think about it for a second. If we use the free body diagram considering him and the platform as our system we know that the summation of F will be equal to 2T minus M1 plus M2 multiplied by G. All of this will be equal to M1 plus M2 all multiplied by A. That means that the acceleration A is equal to 2F minus M1 plus M2G divided by M1 plus M2. This is the expression for the acceleration of the system. Now the next question would be what is the force that he asserts on the platform? Remember that F is given F is 300. M1 is 40 kilograms, M2 is 20 kilograms and let's take G to be 10 to make our calculation simple. If we insert all of that there we will have the acceleration A equal to M2 multiplied by 300 Nm minus 40 plus 20 multiplied by 10 all divided by 40 plus 20. 40 plus 20 is 60 times 10 that will give us 600 divided by this is equal to 0. In other words the acceleration of the system is 0. What does that imply? It means that the platform and the person have been pulled up with a constant speed. That is a good revelation. Now the next question is to calculate the force that he asserts on the platform. If the acceleration of the system is 0 it essentially implies that the sum of forces acting on him the person is which is equal to N 21 plus T minus M1G will be equal to 0. In which case this implies that N21 will be equal to M1G minus T which will be equal to 400 minus 300 N in other words the force that he asserts on the platform is equal to 100 N. This is a good one is equal to 100 N. Remember that the acceleration of the system is 0 that would mean if A is equal to 0 this would mean that 2T minus M1 plus M2G is equal to 0. In other words 2T is equal to M1 plus M2G which means that T is equal to 1 half M1 plus M2 all multiplied by G. So this is the expression for the tension in the string that will cause the system to be pulled up with a constant speed. And if we add all of that this will be 1 half 40 plus 20 multiplied by 10. This is 60 times 10. This is 600. This will be 300 N which is the force he asserts on the platform meaning that he pulls himself up with a constant speed. This was actually one of the questions of given in examinations several times. So please if you have any questions regarding your understanding of this problem ask in the discussion forum below and we will be able to help you. Thank you so much and remain blessed.