Homework Help: Pulleys, displacement by vertical height

1. Mar 14, 2016

Hebel

• Member warned to show effort in an attempt at solution when posting a homework question.
1. The problem statement, all variables and given/known data
(see attached diagram)

2. Relevant equations
(see attached diagram)

3. 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.

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Last edited: Mar 14, 2016
2. Mar 14, 2016

SteamKing

Staff Emeritus
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?

3. Mar 14, 2016

BvU

Hi Hebel,

Have you read the guidelines ? In particular the part

[hint] How much does A go up when B moves down 2h ?

4. Mar 14, 2016

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.

5. Mar 14, 2016

SteamKing

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

6. Mar 14, 2016

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?

7. Mar 14, 2016

SteamKing

Staff Emeritus
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?

8. Mar 14, 2016

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?

9. Mar 14, 2016

SteamKing

Staff Emeritus
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?

10. Mar 14, 2016

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?

Last edited: Mar 14, 2016
11. Mar 14, 2016

Yes.