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Which weight will lift first as the rope is pulled?

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Re: Which weight will lift first as the rope is pulled?

#61
post #34

I loved these pulley problems in statics. Assume the weights are resting on a surface, the pulleys and rope are massless, the pulleys are frictionless, and the system is maintained in quasi-equilibrium as the rope is pulled (steady state & small accelerations). In this case, the tension T in the rope is constant everywhere. Now, take a horizontal section through the ropes. ("Cut" them and replace the missing portions…

What if T >> 30 right from the start. Don't they all rise at once?

Re: Which weight will lift first as the rope is pulled?

#62
post #47
post #41

Earlier quoted context omitted.

"When ... T = 10, weight A begins to rise". No; the Tension the guy is supporting at rest is bigger than 10 (there are 2 other weights) so at T = 10 he would be moving backwards. He needs to apply a bit more than the tension at rest. (edit: this is for when all 3 weights are in the air, I see now some people see them in a floor that is not drawn)

The bottom of each weight is at about the same level as the bottom of the man's feet. A floor is the natural thing to assume. Otherwise it would be difficult to get them into this configuration.

A good way to think about this is to replace the man with a fourth weight, fixed to the rope (as opposed to a pulley). Now it should be clear that the weights would not rest in that configuration unless they were supported by a floor.

Re: Which weight will lift first as the rope is pulled?

#63
post #34

I loved these pulley problems in statics. Assume the weights are resting on a surface, the pulleys and rope are massless, the pulleys are frictionless, and the system is maintained in quasi-equilibrium as the rope is pulled (steady state & small accelerations). In this case, the tension T in the rope is constant everywhere. Now, take a horizontal section through the ropes. ("Cut" them and replace the missing portions…

What if T >> 30 right from the start. Don't they all rise at once?

It's slightly foolish to think about such an idealized scenario, but I believe that the answer is no, until mass A rises fully, the rope can still slide around masses B and C without needing to apply its tension to moving them upward.
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