Solving for Acceleration in a Complex Pulley System

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    Pulleys System
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Homework Help Overview

The discussion revolves around determining the acceleration of mass m1 in a complex pulley system, where friction is absent and the pulleys are assumed not to rotate. Participants are examining the implications of their equations and the assumptions made regarding the system's setup.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to derive the correct formula for acceleration, with some expressing uncertainty about their equations. Questions are raised regarding the definitions of acceleration variables and the implications of a frictionless pulley. There is a suggestion to start from basic principles, including the assignment of unknowns for tensions and applying the ∑Fi=ma equation for each mass.

Discussion Status

The discussion is ongoing, with participants providing feedback on each other's reasoning and equations. Some guidance has been offered regarding the need for clearer explanations of the equations used, and there is an acknowledgment of the complexity of the problem without friction. Multiple interpretations of the problem setup are being explored, but no consensus has been reached.

Contextual Notes

Participants note the absence of radii for the pulleys, leading to the assumption of a truly frictionless scenario. There is a concern about the clarity of the original poster's equations and the need for a more fundamental approach to the problem.

TheLil'Turkey
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1. Homework Statement
What is the acceleration of m1? There is no friction so the pulleys don't rotate. The top rope is connected to the ceiling.

Homework Equations


See photo. I think my formula for the acceleration of M2 is only right if m1 = m2 and wrong in all other situations, but I'm not sure what the correct formula is.

The Attempt at a Solution


See photo.
 
Last edited:
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In the equation for the acceleration of M2, I forgot to multiply it by g.
I uploaded a more recent photo of my attempted solution. It's in the OP above the original photo.
 
Last edited:
You don't explain the basis for any of your equations, so you need to start at a more basic level. Assign an unknown to each tension and write out the ∑Fi=ma equation for each mass.
By the way, when a pulley is described as frictionless it nearly always means merely that there is no frictional torque at its axis. It does not usually mean there is no friction between the pulley and the rope. (If no friction there then it might as well just be a round mass, no need for it to be a pulley.) Thus, if the pulley has mass and a known radius then you should take into account its moment of inertia. However, if no radius is provided then clearly you have no way to take it into account.
 
There are no radii given. So it's best to assume it's truly frictionless. The problem is difficult enough without friction. If you or anyone else sees any mistakes in my equations I'd appreciate any help you could provide.
 
TheLil'Turkey said:
There are no radii given. So it's best to assume it's truly frictionless. The problem is difficult enough without friction. If you or anyone else sees any mistakes in my equations I'd appreciate any help you could provide.
As I posted, your working is not immediately intelligible because you do not explain how you get any of your equations. Either explain them, or start at a more fundamental level with unknowns for tensions and a ∑F=ma equation for each mass.

You also need to define which way the various acceleration variables are defined. Are they all positive upwards? It doesn't look like it.

For what it's worth, your equations do not smell right to me. I would expect a m1+m2 term in your first equation.
 

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