Dynamics question -- 3 masses on a pulley-rope system on an inclined plane

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Homework Help Overview

The discussion revolves around a dynamics problem involving three masses on a pulley-rope system situated on an inclined plane. Participants are examining the acceleration of the system and the tensions in the ropes, as well as addressing a component related to static equilibrium.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are sharing their calculated values for acceleration and tensions, with some expressing uncertainty about their results. Questions are raised regarding the methodology used to arrive at these values, particularly concerning the effects of mass accelerations and friction. There is also a request for clarification on the static equilibrium aspect of the problem.

Discussion Status

There is an active exchange of calculations and methods, with some participants questioning the assumptions made in their peers' approaches. Guidance is being offered in the form of requests for detailed workings and clarifications on specific equations, indicating a collaborative effort to understand the problem better.

Contextual Notes

Some participants note discrepancies in their calculated values for acceleration, suggesting that assumptions about the system's dynamics may need to be revisited. There is mention of omitted factors such as mass accelerations and friction, which could influence the results.

rabsta00
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Homework Statement
A mass m is 5kg and another mass, M=6kg. Find the acceleration of this system if the kinetic friction is 0.1 and theta = 30 degrees. Find all tensions of connecting ropes. For which values of M will the system stay in an equilibrium position?Assume that the static friction coefficient is 0.15. Disregard the mass of the pulley and ropes.
Relevant Equations
F=ma
Screen Shot 2021-03-29 at 12.31.31 pm.png

This image was provided, I've completed the first part of the question and got a = 4.8m/s^2 as well as T1= 24.5N and T2=34.3N. not sure about my answers though. also I don't understand the mass in static equilibrium part, can anyone explain how to solve that? Thanks.
 
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rabsta00 said:
got a = 4.8m/s^2
I get a far smaller value. Please post your working.
 
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haruspex said:
I get a far smaller value. Please post your working.

IMG_2060.jpg

I tried a different method but ended up getting a = 4.1 which isn't much smaller.
 
You omitted the effect of the mass accelerations and friction on the tensions.
 
rabsta00 said:
View attachment 280501
I tried a different method but ended up getting a = 4.1 which isn't much smaller.
Please take the trouble to type equations in. It makes it much easier to quote lines to comment on.
You have T1=2mg sin(θ)-mg sin(θ). How do you arrive at that?
Your calculation of the acceleration of 2m ignores the string. You just have it sliding down the slope unrestrained.
 

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