Solve 3 Mass, 3 Pulley Homework

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Homework Help Overview

The discussion revolves around a problem involving three masses and three pulleys, specifically focusing on finding the acceleration of each mass. The setup includes a massless, frictionless pulley system with three connected masses, leading to questions about the relationships between their accelerations.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the equations of motion for the system, including tension and gravitational forces acting on the masses. There is uncertainty about how to apply the conservation of string principle and the relationships between the accelerations of the masses. Questions arise regarding the direction of movement and its implications on the accelerations.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some guidance has been offered regarding the direction of movement and the implications for the accelerations of the masses. However, there is no explicit consensus on the relationships among the accelerations yet.

Contextual Notes

Participants note the importance of consistency in assuming the direction of movement for the masses. There are also mentions of multiple possibilities for which mass could be accelerating downward, indicating a need for further clarification on the setup.

jkw
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Homework Statement


--------------
I I I = string
O O O = massless frictionless pulley
I II I
' O " . = mass 1
: : = mass 2
" = mass 3

Find acceleration of each mass.

Homework Equations


F=ma
conservation of String

The Attempt at a Solution


Tension is same
T-m1g = m1a1
2T-m2g = m2a2
T-m3g = m3a3

a1=a3=1/2a2 <- I am not sure how to use conservation of string... shouldn't a1 is equal to a3 because there are connected to same sting..
so my question is how to get relationship between/among accelerations
 

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Last edited:
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jkw said:

Homework Statement


--------------
I I I = string
O O O = massless frictionless pulley
I II I
' O " . = mass 1
: : = mass 2
" = mass 3

Find acceleration of each mass.

Homework Equations


F=ma
conservation of String

The Attempt at a Solution


Tension is same
T-m1g = m1a1
2T-m2g = m2a2
T-m3g = m3a3

a1=a3=1/2a2 <- I am not sure how to use conservation of string... shouldn't a1 is equal to a3 because there are connected to same sting..
so my question is how to get relationship between/among accelerations

Once you assume the direction, you have to be consistent with it.
I quess you assume m2 is going down.
Thus m2g is greater then 2T.

Add: There 3 possibilities of movement. m1 or m2 or m3 accelerating downward.
 
Last edited:
Hoi jaw, welcome to PF.
When m2 moves through a distance x in tthe downward direction, how much m1 and m2 move in the upward direction?
 
If m2 move downward by x
Then should it be m1 move up by x/2 and m3 move up 1/2.
Since string is constant <length
a1+2a2+a3=o

Am I right?
 

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