Acceleration in a Weight Machine

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Homework Help Overview

The discussion revolves around an Atwood's machine problem involving two masses connected by a string over a pulley. The challenge is to determine the acceleration of the masses while considering the mass and radius of the pulley.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the use of tension and forces acting on the masses, as well as the rotational dynamics of the pulley. There are attempts to derive equations involving the moment of inertia and the relationship between linear and angular acceleration.

Discussion Status

Some participants have suggested using Newton's second law for each mass and the rotational equation for the pulley. Others have expressed uncertainty about the correct application of the moment of inertia and how to incorporate the mass of the pulley into the equations. There is a recognition that a more thorough approach is necessary to arrive at a solution.

Contextual Notes

Participants note the importance of deriving equations rather than relying on found equations, indicating a focus on understanding the underlying principles. There is also mention of the need to consider the rotational dynamics of the pulley, which adds complexity to the problem.

eagles12
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Homework Statement



An Atwood's machine consists of two masses, m1 and m2, connected by a string that passes over a pulley.
If the pulley is a disk of radius R and mass M, find the acceleration of the masses.
Express your answers in terms of variables m1,m2, M, R, and appropriate constants

Homework Equations



T-mg=ma

The Attempt at a Solution



a=-g/(1+I/(m1+m2)R^2
this is an equation i found but i am not sure what to do with I
 
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hi eagles12! :smile:

(try using the X2 button just above the Reply box :wink:)
eagles12 said:
this is an equation i found but i am not sure what to do with I

you mean you found it on a website? :rolleyes:

(it doesn't look right, but anyway …)

you need to call the tension T, and do F = ma twice (once for each mass), and τ = Iα for the pulley, and then eliminate T …

what do you get? :smile:
 
eagles12 said:

Homework Statement



An Atwood's machine consists of two masses, m1 and m2, connected by a string that passes over a pulley.
If the pulley is a disk of radius R and mass M, find the acceleration of the masses.
Express your answers in terms of variables m1,m2, M, R, and appropriate constants

Homework Equations



T-mg=ma

The Attempt at a Solution



a=-g/(1+I/(m1+m2)R^2
this is an equation i found but i am not sure what to do with I
It is not a good idea to find an equation without doing some work to arrive at the solution. Please make an attempt. The I for the pulley is the least of your problems.:frown:
 
The correct answer can be found here:
http://en.wikipedia.org/wiki/Atwood_machine

but I agree with the others you need to find a way to it, that's the point. My guess is that looking at the energy balance is a shorter way in this problem.
 
Well i found that equation from a similar problem in my textbook and then altered it for my problem
 
I am still having trouble figuring out how to use the M (mass of the pulley) because i need it in my equation.
i tried a=g m1-m2/m1+m2
 
I guess you are missing the pulley rotation equation: I \dot{\omega} =(T2-T1)R
where I is the pulley torque and equals MR^2, (omega)'=a/R. T1 and T2 are the tension forces on both sides. acceleration of m1 and m2 is a.
Now you should have three equations: the second Law for m1, the second law for m2 and the rotation equation for the pulley.
 

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