Inclined Plane(s) Involving Forces

[culex-knight]

Homework Statement

Literally #19 from this link: http://physics.ucsd.edu/students/courses/summer2007/managed/physics2a/documents/chp6.pdf

The figure is not within the .pdf file, so I recreated the figure it references: http://img32.imageshack.us/img32/5701/figurephysics.png

Homework Equations

$$F = ma$$

The Attempt at a Solution

Working the problem on my own, I only am able to get to this step, where the tension forces cancel:

$$m_ra + m_la = m_rg\sin(20) - m_lg\sin(60)$$

... I am at a loss for the next step; particularly in the demonstrated solution, where they add and subtract the acceleration.

 

[Delphi51]

mr*a + ml*a = mr*g*sin(20) - ml*g*sin(60)
Take all the mr terms to the left side:
mr*a - mr*g*sin(20) = -ml*g*sin(60) - ml*a
Too many minus signs so multiply everything by -1
mr*g*sin(20) - mr*a = ml*g*sin(60) + ml*a
Factor out the mr on the left side:
mr[g*sin(20) - a] = ml*g*sin(60) + ml*a
Divide both sides by the [ ] part
mr = ml*g*sin(60) + ml*a all divided by [g*sin(20) - a]