# 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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