# Pulley system

1. Oct 26, 2008

### asi123

1. The problem statement, all variables and given/known data

Hey guys.
look at this pulley system.
I drew all the forces, and also, the pulleys have no mass and so as the rope.
What do you say about the equations I wrote, are they right?
And BTW the first part of the question is to figure which mass has acceleration bigger then g and they say you can figure it out with out solving the equations, any idea?

2. Relevant equations

3. The attempt at a solution

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2. Oct 27, 2008

### tiny-tim

Hi asi123!

If the last equation is a3 = 2a2 = 2a1, then it's wrong.
erm … T > 0, so isn't it obvious?

3. Oct 27, 2008

### asi123

I meant the size of the accelerations, not direction, isn't that right?
Maybe it's a3 = a2 = 2a1 ?

4. Oct 27, 2008

### tiny-tim

No, you should be getting one equation, not two …

you only have one principle to help you … the conservation of the length of the string!

5. Oct 27, 2008

### asi123

Yeah, you right, it's pretty obvious, by the equations we can see than m2 accelerate faster then g.

I don't quite understand the principle of the length of the rope, can you please help me with it?
I mean, what is the connection between the length of the rope and the acceleration?

Thanks.

6. Oct 27, 2008

### tiny-tim

The rope starts at m2, and finishes at m3.

Call the positions x1 x2 and x3. What is the length of the rope in terms of x1 x2 and x3?

Then differentiate twice.

7. Oct 27, 2008

### asi123

I'm sorry, I don't understand what you mean by x1, x2 and x3.
Do you mean for example that x1 is the length between m1 and m2 or something like that?

8. Oct 27, 2008

### tiny-tim

Any three parameters will do.

Personally, I'd choose the height from the ceiling, but your suggestion will work also.

9. Oct 27, 2008

### asi123

Ok, one second, am I right to say a3 = 2a1 ?

10. Oct 27, 2008

### tiny-tim

only if a2 = 0 … which it isn't!

(you're trying to oversimplify! )

11. Oct 27, 2008

### asi123

What do you mean you choose the height from the ceiling? something like I drew in the pic?

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12. Oct 27, 2008

### tiny-tim

(i can't see the pic yet)

I mean the height of each mass below the ceiling.

13. Oct 27, 2008

### asi123

Well, how can you obviously know that? it's not like they are telling you "this mass is 30 cm beneath and the other on is 60 cm...", I mean, how can you measure that?

Thanks by the way

14. Oct 27, 2008

### tiny-tim

You're welcome!

"how can you obviously know that?"… you don't know … that's why they're called unknowns!

15. Oct 27, 2008

### asi123

Well, if you don't know, than how can you find the connection between the accelerations of the masses?
Do you see the pic I posted by the way?

16. Oct 27, 2008

### tiny-tim

(still no pic)

Because there is an equation for the lengths of the string, between the masses, in terms of x1 x2 and x3.

17. Oct 27, 2008

### asi123

Ok, I didn't quite get it, but thanks anyway.