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## 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 m

_{1}moves 1 meter, m

_{2}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 m

_{1}, m

_{2},

*θ*, and g.

## Homework Equations

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

ΣF

_{1}=m

_{1}a

_{1}=m

_{1}g-T

ΣF

_{2}=m

_{2}a

_{2}=T-m

_{2}gsinθ

## 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*(m

_{1}-m

_{2}sinθ)/(m

_{1}+m

_{2}). 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, m

_{1}will accelerate twice as fast as m

_{2}, 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.