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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?

#31

Post by brlewis »

RiderOfGiraffes wrote: post #20
brlewis wrote: post #17

Earlier quoted context omitted.

Your conclusion is incorrect given your assumptions. You are assuming no floor, in which case all the weights will rise. Only the man will fall. I think the problem was intended to include a floor that simply isn't drawn.

Do you really want me to write the full six page analysis? No, I didn't think so. Unfortunately, concise replies such as the one I gave and which require the reader to think a little often result in replies such as yours where it is difficult to discern whether you are being deliberately clever, deliberately trollish, or genuinely confused. Let me expand. I only assumed the weights were unsupported, not the man. I di…

I'm not trolling, and only half joking. Your first paragraph where you talked about the heavier weight falling seemed like a joke about the drawing not including a floor. Which would be fine, except someone making that silly assumption should go all the way with it and assume the man is unsupported too.

Now I understand that you were helping people understand the analysis, and I'm sorry my reply sounded trollish.

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

#32

Post by barrkel »

lazyant wrote: post #25

The length of the rope is constant. For every weigh with a pulley the weigh moves 1/2 length unit for every length unit it's being pulled. Weights don't matter; C will go up first, then B then A (at a relative 1/2 length ratio).

Assuming frictionless rope, pulleys, non-stretchable rope, etc. etc., and assuming the system is at rest, with weights on the ground.

The tension (call it T) in the rope is the force that is acting on each pulley; since the rope is wrapped around all pulleys exactly once, the force applied to every weight is 2T (assuming the fixed pulleys attached to the ceiling aren't going anywhere). If 2T isn't larger than the force of gravity for any one of the weights, then nothing is going to happen. If the man applies enough force (T), the first weight to lift up is the weight whose force of gravity (mass times g) is exceeded by 2T. Since the force of gravity is proportional to the mass, the weights do indeed matter; the lightest weight rises first.

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

#33

Post by brlewis »

amalcon wrote: post #18

This reminds me of the airplane on the conveyor belt, in that the only confusion comes from the question being insufficiently specified. - Friction of the pulleys - Mass of the pulleys - Moment of inertia of the pulleys - Mass of the rope - Unit of mass of the weights - Is there a surface that the weights are resting on? - What's the local gravity like? - Others If we assume the things we're likely supposed to (rope…

The airplane on the conveyor belt is more interesting in this respect, in that different people have different ideas about how the question should be interpreted.

For this question, I think everyone will agree on the likely expected assumptions. Incidentally, the mass of the rope doesn't affect the answer so long as it's uniform, and the mass of the pulleys doesn't matter so long as the pulleys directly attached to the weights all have the same mass. And once you assume the pulleys are frictionless, their moment of inertia doesn't affect the answer either.

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

#34

Post by mkn »

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.)

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

#35

Post by mcn »

RiderOfGiraffes wrote: post #2

If the system is frictionless, the rope is weightless, and the weights are not supported, then the lighter weight will rise and the heavier weight(s) will fall. Therefore if the rope is pulled very slowly, the lighter weight will rise first. If the rope really is weightless and the pulleys really are fictionless (and inertialess) then it doesn't matter how hard or fast you pull, the lighter weight will rise first. Th…

>If the rope really is weightless and the pulleys really are fictionless (and inertialess) then it doesn't matter how hard or fast you pull, the lighter weight will rise first.

I'm considering a thought experiments that make me believe that this is not the whole story.

Imagine a two weight system set up similar to the original diagram in which the weights are the same weight, and the gravity is very little. Yanking on the rope I imagine them rising at the same speed. Now, we take a very small flake off of one weight and repeat the experiment. It seems clear that both weights will still rise from the start, just the lighter weight will rise at a faster speed.

I think this should extend to three weights of any positive mass -- if you yank the rope fast enough (and it might be very fast) all three should rise from the start.

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

#36

Post by lazyant »

barrkel wrote: post #32
lazyant wrote: post #25

The length of the rope is constant. For every weigh with a pulley the weigh moves 1/2 length unit for every length unit it's being pulled. Weights don't matter; C will go up first, then B then A (at a relative 1/2 length ratio).

Assuming frictionless rope, pulleys, non-stretchable rope, etc. etc., and assuming the system is at rest, with weights on the ground. The tension (call it T) in the rope is the force that is acting on each pulley; since the rope is wrapped around all pulleys exactly once, the force applied to every weight is 2T (assuming the fixed pulleys attached to the ceiling aren't going anywhere). If 2T isn't larger than the for…

the problem states what happens "if you pull", it's assumed that the guy can pull, otherwise you are right and weighs matter

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

#37

Post by lazyant »

loup-vaillant wrote: post #30
lazyant wrote: post #26

Earlier quoted context omitted.

funny the right answer being downvoted without reason

You go against the consensus without a solid explanation. For instance, why don't the weights matter? Would they matter if they were respectively 1mg, 1kg, and 1megaton?

Fair enough. I gave the summarized version. I'll try to explain better.

I'll only take basic classic mechanics assumptions: that the rope is of constant length (ie is like a cable that doesn't compress or expand). The framework is quasi-static classical mechanics; the results of the guy pulling slowly a little bit can solve the problem or be generalized (I won't consider the situation of the guy jerking quickly the rope etc).

The guy's hand is under a calculable tension Tw that will be 60 units or whatever, it doesn't matter. The problem asks what happens when the guy pulls, so we suppose that he's not the one being pulled but he moves forward to the right. The tension Tg that he applies doesn't matter; as long as it's bigger than the one from the weights (Tg > Tw) he'll move the rope (we discard friction since he moves slowly or if you take into account friction he just needs more force, it doesn't matter). So the distribution of weights or their actual measure don't matter so far. (of course if you have a million tons and you blow the guy away weighs matter).

Now since the cable/rope has constant length (there are no slacks etc since it's moving) when the guy pulls 1mm then than length needs to be taken from somewhere in the pulley systems.

The effect of a pulley is to divide the length of rope you take in two (one has to go to the left vertical part of rope and the other one to the right one); this is why the tension in each side of a pulley is 1/2 of the total tension and you can pull with 1/2T a weight of T with a pulley. So with this we can straightforwardly calculate the tensions everywhere but we don't need that.

So the that 1mm is taken from the system and the more pulleys the rope has to go through the less is taken (because of this 1/2 I explained above), so the weight closer to the guy (with less pulleys) will raise first, then the next one in the middle, then the next one etc; weighs don't matter.

clarification update: poor conclusion wording: if weights are in the air all 3 weights go up at the same time but C will move more than B and B more than A.

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

#38

Post by lolipop1 »

cynicalkane wrote: post #23
lolipop1 wrote: post #13

Earlier quoted context omitted.

Is the person currently pulling, are the weights on the ground, are the weigths currently moving to get into a stable position? Friction, weight of cord, acceleration, etc. etc. Any combination of the previous? Depending on your level with maths/physics you'll probably give different answers and make different assumptions.

In physics problems things are assumed idealized unless they aren't. Also, velocity doesn't matter here, and no math is required to solve the problem.

I didn't know physics problems are assumed to be idealized... When you build a bridge for example, will the physics try to be simplified to the max? (Honest question here).

Velocity would matter -- it seems to me -- if there is friction and probably a few other factors included like elasticity. No?

Personally, I always considered physicists to be applied mathematicians (not the other way around although I've seen physics problems thrown in university level math classes). That's why I put that there, so assuming a high level of math skills, you'd probably change your way of thinking quite a bit.

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

#39

Post by amalcon »

brlewis wrote: post #33
amalcon wrote: post #18

This reminds me of the airplane on the conveyor belt, in that the only confusion comes from the question being insufficiently specified. - Friction of the pulleys - Mass of the pulleys - Moment of inertia of the pulleys - Mass of the rope - Unit of mass of the weights - Is there a surface that the weights are resting on? - What's the local gravity like? - Others If we assume the things we're likely supposed to (rope…

The airplane on the conveyor belt is more interesting in this respect, in that different people have different ideas about how the question should be interpreted. For this question, I think everyone will agree on the likely expected assumptions. Incidentally, the mass of the rope doesn't affect the answer so long as it's uniform, and the mass of the pulleys doesn't matter so long as the pulleys directly attached to t…

True. The airplane problem had several things that were ambiguous; this problem only has things that are unspecified.

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

#40

Post by cynicalkane »

lazyant wrote: post #37
loup-vaillant wrote: post #30

Earlier quoted context omitted.

You go against the consensus without a solid explanation. For instance, why don't the weights matter? Would they matter if they were respectively 1mg, 1kg, and 1megaton?

Fair enough. I gave the summarized version. I'll try to explain better. I'll only take basic classic mechanics assumptions: that the rope is of constant length (ie is like a cable that doesn't compress or expand). The framework is quasi-static classical mechanics; the results of the guy pulling slowly a little bit can solve the problem or be generalized (I won't consider the situation of the guy jerking quickly the r…

When a weight is at rest, the tension in the rope must be less then or equal to half the weight. The problem asks which weight will be first to not be at rest. The answer should now be obvious.
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