Help with a pulley problem with 3 masses

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The discussion revolves around solving a pulley problem involving three masses with different accelerations. Participants emphasize the need for additional equations to relate the tensions and accelerations of the masses, particularly highlighting the relationships derived from the massless pulleys. A key point is the differentiation of the total string length to establish connections between the accelerations of the masses. The conversation also addresses the correct assumptions regarding tension in the strings and the direction of accelerations. Ultimately, the group arrives at a consensus on the equations governing the system, leading to a solution for the acceleration of the masses.
  • #31
haruspex said:
It seems each acceleration is being taken as positive in the likely direction of movement: 1 to the right, 2 to the left, 3 down.
For each unit of distance 1 advances, 3 drops 1 unit.
For each unit 2 advances, 3 drops 2 units.
Thanks @haruspex but I still don't understand
if "For each unit of distance 1 advances, 3 drops 1 unit" this means that ##|\vec{a_1}|=|\vec{a_3}|## right?
Also I don't understand how the following holds:
"For each unit 2 advances, 3 drops 2 units"
 
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  • #32
Delta2 said:
Thanks @haruspex but I still don't understand
if "For each unit of distance 1 advances, 3 drops 1 unit" this means that ##|\vec{a_1}|=|\vec{a_3}|## right?
Only if 2 stays put. Similarly, 3 dropping 2 for each unit 2 moves is on the assumption that 1 stays put.
So in algebra it's ##\frac{\partial a_3}{\partial a_1}=1## etc.
 
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