3 ms·
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
by mkn 16y ago
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 of the rope with the tension.) Each weight is experiencing an upward force of 2T.
When 2T >= 20, or T = 10, weight A begins to rise. Once a hits a stop, T must be increased to just above 20 to get Weight B to rise. Similarly, T just above 30 causes C to rise after B stops.
The "trick" with these pulley problems is to section the problem through the cables and show the tension, T. Then you've just got free body problems, in this case subject to the floor constraint.
Oh, also, while the first weight is being lifted, the floor beneath weight B experiences 40 - 20 = 20 units of force, and the floor under C experiences 60 - 20 = 40 units of force. Once B is lifted, the floor under C experiences 60 - 40 = 20 units of force. (Presuming that the labels are weights, and not masses.)
- lazyant 16y ago"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)
- brlewis 16y agoThe 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.
- leif 16y agoA 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.
- lookACamel 16y agoThere must be a floor ... or maybe the man is floating!
- lookACamel 16y agoWhat if T >> 30 right from the start. Don't they all rise at once?
- leif 16y agoIt'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.