Relationship of acceleration of masses in pulley

[drragonx]

Homework Statement

Find the relationship of acceleration between the masses, m1, m2 and m3 where m1>m2>m3.

The question has a free pulley in the left attached to mass m1. then goes through a fixed pulley , through a free pulley that is attached to m2 and then through a fixed pulley, with the end of the string attached to mass m3.

Homework Equations

The Attempt at a Solution

my professor came up with: a1-a2+2(a3)=0 while i came up with 2(a1)-2(a2)-a3=0

 

[nasu]

Without a drawing it's difficult to "see" the setup.
What "goes" through a fixed pulley? Not the free pulley, I suppose.
Isn't the rope attached to a wall or ceiling on the left?

 

[drragonx]

heres the image

 

[BiGyElLoWhAt]

Are you allowed to use a Lagrangian? Or just N2L?

 

[BiGyElLoWhAt]

(Also, that would be good info to put under relevant equations)

 

[nasu]

I think m3 have the larger acceleration so your equation looks better to me.
However the signs do not look so good.
If both m1 and m2 move with the same acceleration (downwards for example) it would result that a3 is zero which is not what happens.

 

[BiGyElLoWhAt]

m1 and m2 cannot both move downward. the only way m1 can move down is if m2 moves up, giving m1 the freedom to move down (it can't move down without taking the rope with it)

 

[nasu]

Yes, they can. They both "take rope" from m3 which moves up.
It depends on the masses.

 

[BiGyElLoWhAt]

Hmmm... somehow I neglected the fact that m1 and m2 were held up via pulleys attached to them... sorry about that.

 

[drragonx]

as per my prof's explanation, we are allowed to assume any sensible motion for the masses. so here, both equations assume m2 and m3 are moving up while m1 is moving down. The general method to solve these equations, as per my prof's suggestion, is to find the displacement. So, for the following question, 2(x2)=x1+x3, which when differentiated becomes 2(a2)=(a1)+(a3)

 

[nasu]

But this is a different problem. Are you done with the first one?

 

[drragonx]

im just saying they both are related in the way we solve them. This question's answer is certain but not the first one. I posted the question so that you get the idea of it.

 

[drragonx]

also, i recently found out that m1=16kg, m2=8kg, m3=2kg