Pulley on an inclined plane

Homework Statement

A frictionless pulley connects 2 masses, one of which is on a frictionless inclined plane at angle θ, as shown in the diagram. The pulley system is set up so it has a mechanical advantage of 2 (so that if m1 moves 1 meter, m2 will move only 0.5 meters). Find equations that give the acceleration of each mass as well as the tension in the rope in terms of m1, m2, θ, and g.

Homework Equations

T=tension in the rope, subscripts indicate which mass the variable is referring to

ΣF1=m1a1=m1g-T
ΣF2=m2a2=T-m2gsinθ

The Attempt at a Solution

This problem is easy if it is a simple pully, since both accelerate at the same rate of a=g*(m1-m2sinθ)/(m1+m2). To get this you just have to add the above two equations and solve for a. But since there is a mechanical advantage of 2, m1 will accelerate twice as fast as m2, and thus you cannot simply add the equations to find the acceleration. I am not quite sure how to approach this problem, and any help would be appreciated.

Attachments

• pulley.JPG
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