Acceleration in a Weight Machine

[eagles12]

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

 

[tiny-tim]

hi eagles12!

(try using the X² button just above the Reply box )

this is an equation i found but i am not sure what to do with I

you mean you found it on a website?

(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? ​

 

[PhanthomJay]

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.

 

[ivanis]

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.

 

[eagles12]

Well i found that equation from a similar problem in my textbook and then altered it for my problem

 

[eagles12]

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

 

[ivanis]

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.