Relationship of acceleration of masses in pulley

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Homework Help Overview

The discussion revolves around understanding the relationship of acceleration between three masses, m1, m2, and m3, in a pulley system where m1 is greater than m2, which is greater than m3. The setup involves both free and fixed pulleys, with specific constraints on the motion of the masses.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants explore different equations relating the accelerations of the masses, with some suggesting the use of Lagrangian mechanics versus Newton's second law. There are questions about the setup, particularly regarding the movement of the masses and the implications of their respective accelerations.

Discussion Status

Participants are actively engaging with the problem, sharing equations and discussing the implications of their assumptions. Some guidance has been offered regarding the relationship between the accelerations, but there is no explicit consensus on the correct approach or solution yet.

Contextual Notes

There are constraints regarding the assumptions that can be made about the motion of the masses, as well as the need for clarity in the setup, which is complicated by the presence of multiple pulleys. The specific masses of m1, m2, and m3 have been provided, but their influence on the acceleration relationship is still under discussion.

drragonx
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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
 
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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?
 
heres the image
 

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Are you allowed to use a Lagrangian? Or just N2L?
 
(Also, that would be good info to put under relevant equations)
 
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.
 
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)
 
Yes, they can. They both "take rope" from m3 which moves up.
It depends on the masses.
 
Hmmm... somehow I neglected the fact that m1 and m2 were held up via pulleys attached to them... sorry about that.
 
  • #10
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)
 

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  • #11
But this is a different problem. Are you done with the first one?
 
  • #12
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.
 
  • #13
also, i recently found out that m1=16kg, m2=8kg, m3=2kg
 

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