The document describes two monkeys, Chimpoo and McZee, climbing a rope together. Chimpoo can tolerate a maximum tension of 30 N on his tail. McZee weighs 2 kg. To carry McZee with him as they climb, Chimpoo must apply a force on the rope between 70 N and 105 N, as determined using Newton's Third Law and analyzing the forces as an interacting system accelerating upwards.

1. Chimpoo and McZee I see what you two naughty monkeys are doing … So , climbing is fun for you right… copyrights © youmarks.com

2. Now see what they have done… The McZee shown in the figure is holding the tail of Chimpoo who is climbing upwards the rope. The masses of Chimpoo and McZee are 5 kg and 2 kg respectively. If Chimpoo can tolerate the tension of 30 N, what force should it apply on the rope in order to carry the McZee with it. copyrights © youmarks.com

3. And you McZee cant you climb on your own? copyrights © youmarks.com

4. Suppose Chimpoo had to climb alone on the rope, what would he had done? He would have pulled the rope downwards and the rope would have pulled him upwards …But now he has to support McZee , so he has to apply more force to carry him upwards to right? Now his tail can tolerate a maximum tension of 30 N and McZee weight is 20 N. So , it should not be difficult to carry him. But how come when he pulls the rope upwards and McZee pulls his tail downwards both rope and tail tries to move monkey upwards? Can you explain how? Very simple….Any law that you guys can associate??? Come on guys… copyrights © youmarks.com

5. Yes it was you My Man….You remember his third law….. copyrights © youmarks.com

6. Yea that is Every action has an equal and opposite Reaction copyrights © youmarks.com

7. So yes our monkey applies an ACTION to the rope which in turns gives REACTION back to the monkey pulling it upwards. Also remember Action and Reaction are equal and opposite forces. Now do it for McZee applying action And Chimpoo giving him the reaction Come on pal.. Make this pair yourself.. copyrights © youmarks.com

8. Applying Newton’s Third Law now copyrights © youmarks.com

9. So what are we waiting for now Free Body Diagrams are here my friend…… And you have seen the last slide yea? So, does it sounds difficult now? Also since both are acting as a system , imagine they both are moving upwards at an acceleration , a upwards copyrights © youmarks.com

10. All right let me do it this time for you  Just balance the forces for it T- T 1 – m 1 g = m 1 a  F=T 1 T 1 - m 2 g = m 2 a Now , if we are acceleration , tension T 1 can go maximum upto 30N, putting it as 30 N, we get Tension T as 105 N. But suppose , we don’t want them to accelerate, then T 1 = 20 N which Chimpoo can support . Solving through this we get T=70 N So, T varies between 70 and 105 Newton. copyrights © youmarks.com

11. Let us explain more telling you a story  Shall we…… So Chimpoo and McZee. What are they talking with each other? And can ropes talk? Lets find it out…… copyrights © youmarks.com

12. copyrights © youmarks.com McZee hold on, let me ask the rope if rope can pull us both upwards. Chimpoo pull me upwards…. . Rope Chimpoo, I can pull you upwards and for that you would not have to apply much force as I need to support your weight but to give you the support , I need some input from you which is your Action ( Mr. Newton told me to do so…)

13. You don’t understand rope. If I just give you an action equal to my weight which is 50N, you would not be pulling me with a force which is required to pull both of us together. What is the minimum force you need to pull both of us together? Rope Well , I have to atleast support your weight right? Which is atleast total of your weights which is 50 + 20 = 70 N copyrights © youmarks.com

14. Let me see how much McZee pulls me down because if he pulls me down with a force more than 30 N , I will die anyways. Don’t worry Chimpoo , my weight is 20N only and I am currently putting an action of 20 N only. So, your tail is not going to break out. . Thank God , So rope I can atleast hold McZee for another 10 N. Suppose McZee applies more force that is 30 N , how much I have to pull you down. Chimpoo that is a question which I will answer I think it would then allow me to move ahead as 20 N would go in supporting my weight and remaining 10 N would allow me to accelerate which is 10/ 2 = 5 m/s2. . copyrights © youmarks.com

15. But you accelerate at 5 m/s2, I would also have to accelerate at the same rate right because if I don’t you would just move over me… SO tell me rope how much force I have to apply on you if we both accelerate at 5 m/s2. Rope Pretty easy Chimpoo, I would need 70N to atleast pull you guys together and if you want to accelerat at 5 m/s2, I would need to support you guys for this acceleration too . So an additional force 5 * ( 5+2) = 35 N is needed to support you. So a total of 70 + 35 = 105 N, Can you give me that Chimpoo copyrights © youmarks.com

16. Ok . Rope we now have an option to give you a minimum of 70 N and we can go a maximum till 105 N , we would make sure while climbing , I pull you with a force in that range . Rope Thanks Chimpoo.. Happy Climbing ahead. copyrights © youmarks.com