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Homework Statement
Homework Equations
Conservation of Energy / Virtual Work
$$\sum_i m_i g h_i = 0$$
The Attempt at a Solution
Moving the pulley I labeled A down by ##\delta y## moves ##w## down by ##\delta y##, and moves ##W## up by ##\frac{1}{2} sin\theta##.
So by conservation of energy I have $$-w\delta y + \frac{1}{2}W \delta y sin\theta = 0$$ leading to ##W = \frac{2w}{sin\theta}##.
I feel uncertain about this answer however, because it seems like the mechanics would be the same if you removed Pulley A and replaced it with ##w##.