Pulleys, displacement by vertical height

[Hebel]

Homework Statement

(see attached diagram)

Homework Equations

(see attached diagram)

The Attempt at a Solution

I drew a diagram.What I know. Left part of rope is fixed to ceiling so extra rope comes 'from the right' i.e. 'falls down' as pulley is pulled. I also know that rope is conserved.

 

[SteamKing]

Homework Statement

(see attached diagram)

Homework Equations

(see attached diagram)

The Attempt at a Solution

This problem's solution is 2h, but I don't understand how?

Why don't you make a sketch? Remember, the left-most line is fixed to the ceiling. Where must the extra rope come from when the left sheave is pulled down?

 

[BvU]

Hi Hebel,

Have you read the guidelines ? In particular the part

Do not simply post images of the problem statement or your work.
While posting images may be convenient for you, it's actually one of the most effective ways of getting your request for help ignored. Images are often too big, too small, rotated, upside down, out of focus, dimly lit, or of otherwise poor quality, and your handwriting probably isn't as easy to read as you think it is. Images are a hindrance to the helpers as portions of the problem statement or your work can't easily be quoted. Using images also doesn't qualify as filling out the homework template, so your post may be deleted.

So type up the problem statement and your work. Think "If I can't be bothered to spend my time typing it, why should they be bothered to spend their time reading it?" Use scans or photos for supporting figures. You may, of course, attach an image of the problem statement in addition to the typed version; in fact, if it's a complicated or long problem, you probably should. But you should always provide a typed version as well.

You had help for your first thread, and apperently now for your second too, but still...[hint] How much does A go up when B moves down 2h ?

 

[Hebel]

Hmm that's a good point. I will keep that in mind and apologize for my rudeness.

Well I tried using an energy argument:

i.e. G.P.E --> K.E., but there are just too many variables, as I don't know the masses of either of the bodies involved etc.

Why isn't it just 2h as well?

I can't seem to relate the movement of A to the movement of B... I know that A is attached to a pulley, which has to have some kind of significance.

 

[SteamKing]

Hmm that's a good point. I will keep that in mind and apologize for my rudeness.

Well I tried using an energy argument:

i.e. G.P.E --> K.E., but there are just too many variables, as I don't know the masses of either of the bodies involved etc.

If both masses were zero, that would not affect the answer to this problem in the slightest.

Why isn't it just 2h as well?

I can't seem to relate the movement of A to the movement of B... I know that A is attached to a pulley, which has to have some kind of significance.

That's why you should make a sketch, as an aid to your imagination.

BTW, the distance sheave A would travel would be the same, regardless of whether a mass was attached. This problem is about conservation of the rope which runs between the sheaves, not about energy or any other such phenomenon.

Think about why a pulley system is considered a machine and where its mechanical advantage comes from.

 

[Hebel]

I updated my question, but I still don't really know how to find a concrete relationship between a vertical height (traversed by pulley) and length of the string?

 

[SteamKing]

I updated my question, but I still don't really know how to find a concrete relationship between a vertical height (traversed by pulley) and length of the string?

For some reason, you have blocked out of your mind how the shaves are going to move at all by changing the lengths of the different parts of the rope running thru them. Remember, it's a single piece of rope connecting the ceiling to mass B. If you tug down on mass A by a distance h, can either of the two parts of the rope holding up this mass not change their length relative to the sheave supporting mass B?

 

[Hebel]

Well the part on the left (supporting A) goes 'up' h and the part on the right 'down' h? So the rope as a whole 2h?

 

[SteamKing]

Well the part on the left goes 'up' h and the part on the right down 'h'? So the rope as a whole 2h?

If you're pulling down on mass A, the two parts of the rope supporting mass A must lengthen by the same amount. When this occurs, what happens to mass B?

 

[Hebel]

B rises by 2h right? Is that because, if one lowers A by h the one part of the rope supporting A needs to gain a length of h and the other part does as well...? I lack experimental experience with this, are there any animations/experiments/resources you know of?

 

[haruspex]

B rises by 2h right? Is that because, if one lowers A by h the one part of the rope supporting A needs to gain a length of h and the other part does as well...?

Yes.