How Do You Solve a Double Atwood Machine Problem with Unequal Masses?

[dsfrankl]

Homework Statement

If the masses for a double Atwood machine similar to the own shown in the attached picture are m1=2.0kg, m2=3.0kg, and m3=8.0kg: (a) what is the magnitude of the acceleration of the system and (b) how would you draw free-body diagrams for this problem?

NOTE: m3 does not tilt. Also, two strings will have two tensions.

Homework Equations

F=ma

The Attempt at a Solution

I found the net force by using: F=8g-3g-2g=3g. Then I added the masses to get 13kg. a=F/m=3g/13kg=2.26m/s^2. The problem however, is that I know my professor won't take this. She'll want to see drawings of FBD first (which I managed to draw FBD for m1 and m2 but am not sure how to draw m3), and for me to use tensions as well. I'm not really sure how to do it that way.

 

[Orodruin]

I found the net force by using: F=8g-3g-2g=3g.

This is the net force on what?

which I managed to draw FBD for m1 and m2

So what did the free body diagrams for m1 and m2 tell you?

am not sure how to draw m3

What forces act on $m_3$?

Furthermore, think about what correlations among the accelerations of the masses that you can write down.

Also note that this is not what would typically be called a double Atwood machine. This is a double Atwood machine:

What you have is actually equivalent to a normal Atwood machine.