System with two boxes and pulleys

[Mcoroklo]

Homework Statement

We have a system which look like this:

http://img535.imageshack.us/img535/9153/16234612.jpg

The two boxes is connected by a wire without mass. The big box on the left has the mass 2m, the small box on the right has mass m.
The right pulley has radius r has mass m, and left pulley has radius 2r and mass 2m. Both pulleys are homogeneous cylinders.

A) Determin the angular velocity of the small pulley when the large box has moved distance h downwards. How is the angular of velocity effected on the radius r?

B) Determin both boxes accelerations and the angular acceleration of both pulleys.

Homework Equations

Standard mechanical and rotational equations.

The Attempt at a Solution

The box and pulley on the left is set to be B.
The box and pulley on the right is set to be A.

We know all values of: radius r and mass m.

1. The attempt at a solution

We have been attempting to solve the situation by the following 4 equations (box A and B movement and both pulleys):

(1) T[a]-m*g=m*a[a]
(2) T-2*m*g=2*m*a
(3) T-T[a] = I*alpha[a] = 1/2 *m*r^2*alpha[a]
(4) T-T[a]=I*alpha = 1/2 * 2*m*(2*r)^2*a

Problem is we 6 unknown and 4 equations, which kind of is a problem..! ;-)

Thanks a lot...

 

[aim1732]

There are no two alpha. Both pulleys rotate with equal angular velocities as there is no slipping in the system. Plus alpha is alpha=a*r.So that clears quite a few variables.

But there is a problem. Why do you consider tension in the portion of string b/w the pulleys as T[a]? Is the right pulley massless? Another variable...

 

[Mcoroklo]

First of all, thanks for your reply.

About the right pulley, it has mass m, just as the right box.. So that dosn't count as a variable! :-)

How does the two tensions work?

 

[aim1732]

i implied a third tension in portion b/w the pulleys. Then you would have four variables with four eqn.