Help with a pulley problem with 3 masses

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Homework Help Overview

The discussion revolves around a pulley problem involving three masses, each with different masses and accelerations. Participants are exploring the relationships between the tensions in the system and the accelerations of the masses, while attempting to derive equations that relate these variables.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the need for additional equations to relate the accelerations and tensions. There are attempts to clarify the implications of the system being weightless and inextensible, and questions arise regarding the assumptions made about the forces acting on the masses.

Discussion Status

The discussion is ongoing, with participants providing hints and suggestions for deriving relationships between the variables. Some participants have expressed understanding of certain equations, while others are still seeking clarification on specific aspects of the problem.

Contextual Notes

There are mentions of constraints such as the inextensibility of the string and the massless nature of the pulleys, which are influencing the reasoning and equations being developed. Additionally, there is a focus on how the accelerations of the masses relate to each other based on their movements.

  • #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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