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rock.freak667

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## Homework Statement

http://img376.imageshack.us/img376/1033/questionii7.jpg [Broken]

The diagram shows a cross-section ABCD of a uniform rectangular block of weight W. The lengths of AB and BC are 2a and a respectively. The edge through A rests against a smooth vertical wall and the edge through B rests on a rough horizontal floor. The coefficient of friction between the block and the floor is [itex]\mu[/itex]. The block is in equilibrium with AB inclined at an angle [itex]\alpha[/itex] to the vertical. Show that the wall exerts a force of magnitude [itex]\frac{1}{4}(2tan\alpha -1)W[/itex] on the block.

Show also that [itex]tan^{-1}(\frac{1}{2}) \leq \alpha \leq tan^{-1}(\frac{1}{2}+2\mu)[/itex]

## Homework Equations

[tex]\tau = \vec{F}\times \vec{r}=Frsin\theta[/tex]

## The Attempt at a Solution

In order to not have friction included, I decided to take moments about B.

The distance of W from B is [itex]\frac{\sqrt{5}a}{2}[/itex] (I think I did that correctly).

The normal reaction at A, R, acts parallel to surface on which B lies.

So the clockwise moment is R*2a and the anti-clockwise moment is [itex]\frac{\sqrt{5}a}{2}W[/itex]

is this correct so far, because I don't think I formulated the distances correctly.

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