Understanding the Motion of Double Pulleys: Exploring Acceleration and Forces

[Carbon123]

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 ?

 

[TSny]

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.

 

[Carbon123]

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?

 

[TSny]

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.