- #1

kieyard

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I'm trying to express this diagram as algebraically as possible so later on I can add real world limitations into my equation and see what other requirements are needed.

I got the first and simplest one which is to be in equilibrium the mass/weight of B has to be 2p-1 times that of A where P is the total amount of pulleys in the system.

I also came to the conclusion that as long as the mass B is no deeper than A it will always be higher up than A as the length of string required to move A distance X on the other pulleys has to be half the one before forming a infinite series approaching X.

However in real life the pulley’s height would have to considered as well as a buffer amount of string/rope due to momentum of pulleys/weights.

I’m also saying that the value of tension in the rope, however not expressed on diagram, is 2p-1 T where P is the number of pulleys to the right of the pulley the rope in question hangs upon. I really need someone to word that better. Haha.

The force acting on the bar would also have to come into consideration as there are real world constraints. But as it is in equilibrium the forces up must equal the forces down so the force acting upon the bar is equal to 1+2p-1 mg. however in real life the pulleys and rope would have a mass too which would need to be considered as variables as the total weight from them will also increase as P increases.

Where I want to go with this. I am hoping to make as many equations as possible including as many variables as possible. The idea is that afterwards I will start to implement a force onto B causing it to accelerate which then causes A to accelerate 2p-1 times faster (less with energy lost to friction etc.) to then accomplish a certain V after it has traveled distance X. however real life constrictions on materials etc. means that to accomplish some tasks the amount of pulleys needs to be changed or the distance X needs to be altered etc. or it can tell me that if we get smaller pulleys that there will be less friction, less weight and the system more viable.

I am wanting to collaborate and build upon the equations and systems together as being a high school student my mathematical and physics knowledge isn’t advanced enough.

Any help would be great. Thanks.