# Pulleys and Inclined Planes

1. Aug 1, 2016

### showzen

1. The problem statement, all variables and given/known data

2. Relevant equations
Conservation of Energy / Virtual Work
$$\sum_i m_i g h_i = 0$$

3. 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 $w$.

2. Aug 1, 2016

3. Aug 1, 2016

### kq6up

Not sure why you are using virtual work either. I would attack this problem with mechanical advantage of a system of pulleys.

Regards,
KQ6UP

4. Aug 1, 2016

### showzen

My reasoning here is that if pulley A is moved down to be even with the anchor point, $w$ will have dropped by the initial length between the anchor and the pully.

5. Aug 1, 2016

### showzen

I see my mistake now! $\delta y$ moves $w$ by $2\delta y$. So $W=\frac{4w}{sin\theta}$, which is what I get from force analysis as well.

6. Aug 1, 2016

### haruspex

That looks good.