How to Derive the Acceleration of Mass A in a Double Atwood Machine?

[JoeBargo]

Homework Statement

I've tried and tried and can't solve this to look like this equation. Please Help!

http://i233.photobucket.com/albums/ee237/biggyjoe210/IMAG0175.jpg

1. Show that the Acceleration of Mass A is given by : (look at picture)

Homework Equations

F = ma

The Attempt at a Solution

So far all I have is a = g(mA-mB)/(mA+mB)

Im lost

 

[Spinnor]

Did you draw any free-body diagrams?

 

[JoeBargo]

Yeah all have tension going up and mg going down except the pulley which has tension up and tension down as well *** mg. The tension of string attaching a and b are the same and c and d are the same.

 

[Spinnor]

Does the following look like I'm on the right track? Six equations in six unknowns.

 

[JoeBargo]

Yeah, I have that down. I solved for the smaller system(mA, mB, mD) for acceleration and tension. I'm guessing x is acceleration. If so that's exactly what I have. I can't get the algebra right or something when I solve for a1 and a2(the two separate accelerations of the strings). I keep getting close to the given formula but I'm messing up somewhere.

 

[cajunboy]

hey do you go to tech??
m having problem with the same question...did you solved it??

 

[Raptorkiller]

the trick is displace one body and see the motion of other bodies eg.if u displace the "Mc" body then the other two bodies(Ma and Mb) will as a whole go down but one of them will go up and other down relative to each other.then draw the free body diagram on each.NOTE: tension in the Mc body will be 2times that of ropes of other two.then write the equations involving T and g.gud luck

 

[nickw12]

I'm also at Tech. I get some of it, but there are like 3 parts to the final equation that I'm missing. I'm still not exactly sure on how to do this.