How Do Double Pulleys Affect Acceleration and Forces in Homework Problems?

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Homework Help Overview

The discussion revolves around a problem involving double pulleys and their effect on the acceleration and forces acting on three masses (m1, m2, and m3). Participants are examining the relationships between the forces and accelerations of the masses as described in the equations provided.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants are questioning the direction of motion for the masses based on the equations given, particularly why m2 and m3 are both described as moving upwards in the equations. There is also discussion about the implications of the sign of acceleration a1 on the motion of m1.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the equations and the assumptions made in the problem setup. Some guidance has been offered regarding the positive direction for forces and accelerations, but no consensus has been reached on the implications of the motion directions.

Contextual Notes

Participants are considering the setup of the problem, including the assumption that the masses are released from rest and the implications of the chosen positive direction for acceleration. There is a focus on understanding how the accelerations relate to each other in the context of the pulley system.

Carbon123
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Homework Statement



A mass m1 is hung on a pulley with another pulley on th eother side with two masses;m2 and m3.Find the accelerations of the masses

Homework Equations


F=M.a
a1=-(a2+a3)/2

The Attempt at a Solution


So in my book ,the solution provided was 2T-m1g=m1a1
T-m2g=m2a2 and T-m3g =m3a3.My question is why did the two equations for mass 2 and mass 3 seems to have both objects to move upwards,shouldn't one move down and one up ?why is the equation of motion like that ?
 
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The book is apparently taking upward as the positive direction for each of the three masses when setting up ΣF = ma.

The accelerations in the equations are accelerations relative to the earth.
m2 and m3 do not necessarily move in opposite directions relative to the earth.
 
But what about m1 which is also 2T-m1g=m1a1 wouldn't that imply that it moves upward and thus the two mass m2 and m3 moves downward relative to the Earth ?(or is it because the a1 is equal to negative a2+a3/2?
 
Assuming the masses are released from rest, if a1 turns out to be a positive number then m1 moves upward. If a1 turns out to be negative then m1 moves downward.
 

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