Solve 3 Mass, 3 Pulley Homework

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The discussion revolves around solving a physics problem involving three masses and a pulley system, focusing on the relationship between their accelerations. Participants clarify that tension is consistent across the system and apply Newton's second law to derive equations for each mass. A key point raised is the conservation of string, leading to the conclusion that if mass m2 moves downward by a distance x, then masses m1 and m3 move upward by x/2. The relationship among the accelerations is established as a1 + 2a2 + a3 = 0, emphasizing the need for consistent directional assumptions. Understanding these relationships is crucial for accurately determining the acceleration of each mass in the system.
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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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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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