How Do You Calculate Acceleration in a Dual Pulley System?

[Boltak]

Hi everyone...

I've been struggling with a physics problem for 2 days now... I'm really not sure what to do.

Problem -
A pair of 10.0 kg masses are suspended from (massless) strings wrapped around a dual pulley. The radius of the smaller shaft on the pulley is half the radius of the larger shaft on the pulley. If the total mass of the pulley is also 10.0kg, and the pulley is considered to be a uniform disk, what is the acceleration (magnitude and direction) of mass ($$m_{1}$$) connected to the larger shaft?

Basically... one 10.0 kg mass is attached on the right side of the small shaft, while other 10.0kg mass is attached to the left side of the bigger shaft.

picture at http://members.cox.net/lorddreg/p9.jpg

I was assuming $$m_{1}$$ would most likely accelerate down.

This is what I have so far... I'm not sure if it is correct or not ...

For $$m_{1}$$ ...
$$\sum{F = m * a_{y} = -T_{1} + m_{1} * g}$$

For $$m_{2}$$ ...
$$\sum{F = m * a_{y} = T_{2} - m_{2} * g}$$

I would appreciate any help!

Thank you

 

[suyver]

This looks like a homework assignment, so I'll give you a hint.

Think about the Moment of Inertia of your system...

Good luck!

 

[himanshu121]

You need a constraint equation to solve the problem i.e the relation between T1 and T2 the two pulleys have same angular acceleration which u can relate with two end of ropes just at the surface of the pulley.

 

[himanshu121]

U got 2 equations, u need the third equation which is constraint equation
Remember
No. of Equations = No. of variables