This is exactly where your simplifications show your lack of knowledge. Pulleys and rope are fine methods of connection and diversion - but are not in any sense loss-less. There are in everyday use some good examples of how the missing elements interact.
Theatres
It is century old technology to suspend items above stages and have them move in and out by the application of man(woman) power. The idea is simple. a bar over a stage might need to have 250Kg of equipment suspended. The cables go up to the grid above the stage, they then move sideways, diverted by pulleys, and then down again. On this end is cradle with 250Kg of weight in it. By the application of hand power, a heavy weight can be moved up and down very simply. However, with the brakes off, it's is quite amazing how much extra weight can be added or removed without the bar starting to run on it's own. Frictional losses in the pulleys are the main issue. The rigidity of the wire rope, the friction of the pulley bearings all conspire against exactly what you need in your design, overcoming inertia and managing momentum.
Theatres
It is century old technology to suspend items above stages and have them move in and out by the application of man(woman) power. The idea is simple. a bar over a stage might need to have 250Kg of equipment suspended. The cables go up to the grid above the stage, they then move sideways, diverted by pulleys, and then down again. On this end is cradle with 250Kg of weight in it. By the application of hand power, a heavy weight can be moved up and down very simply. However, with the brakes off, it's is quite amazing how much extra weight can be added or removed without the bar starting to run on it's own. Frictional losses in the pulleys are the main issue. The rigidity of the wire rope, the friction of the pulley bearings all conspire against exactly what you need in your design, overcoming inertia and managing momentum.
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