Which weight will lift first as the rope is pulled? • Hacker News Board

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

#41

Post by lazyant » Fri, Sep 03, 2010, 5:27 PM UTC

mkn wrote: 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…

"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)

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

#42

Post by cynicalkane » Fri, Sep 03, 2010, 5:28 PM UTC

lolipop1 wrote: post #38

cynicalkane wrote: post #23

Earlier quoted context omitted.

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 phy…

When you build a bridge, that's engineering, not physics. It's a physics convention that unspecified factors are assumed to be unimportant. If they were important, they would be specified.

Anyway, it's implausible that the elasticity of the rope or the friction of the pulleys are going to matter. Unless you have really rusty pulleys, or something.

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

#43

Post by lazyant » Fri, Sep 03, 2010, 5:30 PM UTC

cynicalkane wrote: post #40

lazyant wrote: post #37

Earlier quoted context omitted.

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.

When a weight is at rest the tension in the rope is exactly half its weight.

Problem asks which weight would be first to raise (not "not be at rest" that could be going down) so that's why I'm supposing the guy can pull the whole thing. I'm also saying the first one is C (closer to guy).

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

#44

Post by psycocoffey » Fri, Sep 03, 2010, 5:31 PM UTC

dkokelley wrote: post #22

psycocoffey wrote: post #15

Earlier quoted context omitted.

Assumptions: pulleys: idealized, massless, frictionless rope: idealized, massless, doesn't stretch weights: resting on ground. As tension is applied to the rope, Weight A will be lifted first, until it is lifted to the ceiling. Then Weight B, and finally Weight A. It helps to visualize Weight A as being massless. In that case, there would just be extra slack in the rope, and B&C would not move until the slack was tak…

* Then Weight B, and finally Weight A.* I believe you meant C, correct?

Yes, I meant C. Too late to go and fix it now. Good catch

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

#45

Post by cynicalkane » Fri, Sep 03, 2010, 5:31 PM UTC

lazyant wrote: post #43

cynicalkane wrote: post #40

Earlier quoted context omitted.

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.

When a weight is at rest the tension in the rope is exactly half its weight. Problem asks which weight would be first to raise (not "not be at rest" that could be going down) so that's why I'm supposing the guy can pull the whole thing. I'm also saying the first one is C (closer to guy).

The tension in the rope is greater than 30lbs, yet only one weight moves? I give up.

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

#46

Post by [deleted] » Fri, Sep 03, 2010, 5:40 PM UTC

cynicalkane wrote: post #3

Well, the diagram is impossible unless the weights are all resting on the floor, so let's assume they are. This system will find a steady state only at a local minimum of potential energy, so the lightest weight will be lifted before the heavier two get off the ground.

[deleted]

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

#47

Post by brlewis » Fri, Sep 03, 2010, 5:48 PM UTC

lazyant wrote: post #41

mkn wrote: 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…

"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.

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

#48

Post by lazyant » Fri, Sep 03, 2010, 5:55 PM UTC

cynicalkane wrote: post #45

lazyant wrote: post #43

Earlier quoted context omitted.

When a weight is at rest the tension in the rope is exactly half its weight. Problem asks which weight would be first to raise (not "not be at rest" that could be going down) so that's why I'm supposing the guy can pull the whole thing. I'm also saying the first one is C (closer to guy).

The tension in the rope is greater than 30lbs, yet only one weight moves? I give up.

sorry; I made an edit with a clarification.

Basically if the weights are at rest on the floor then mkn's answer is the correct one. If they are at rest on the air, then my answer is the correct one.

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

#49

Post by brlewis » Fri, Sep 03, 2010, 6:03 PM UTC

mcn wrote: post #35

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 o…

In your thought experiment you make the weight difference so small that otherwise insignificant factors (e.g. friction) take over. Go the opposite direction and make the weight difference enormous.

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

#50

Post by mcn » Fri, Sep 03, 2010, 6:38 PM UTC

brlewis wrote: post #49

mcn wrote: post #35

Earlier quoted context omitted.

>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 o…

In your thought experiment you make the weight difference so small that otherwise insignificant factors (e.g. friction) take over. Go the opposite direction and make the weight difference enormous.

Assuming no friction and given a fast tug of the rope I still don't think the near equal weight would hold still or sink while the other near equal weight flew up quickly.

With the large weight difference, I think the required speed of pulling the rope to make them both rise just becomes impractically fast.

Imagine the system in space - all the weights would move up, so they all have an upward force applied to them from the rope tugging. It's just a matter of pulling so fast that that upward force overcomes gravity.