# Bar in static equilibrium + hydrostatics

1. Jan 27, 2007

### Metaleer

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

A thin metal bar of length L is attached to a pivot point (point A in diagram). The bar is partially submerged in water and it can move freely around an axis that forms a 90 degree angle with the plane of the diagram. The density of the bar is 0.4 g cm^(-3). What percentage of the bar is submerged when it is in static equilibrium?

2. Relevant equations

Vectors are in bold.

F = ma

M = r x F

3. The attempt at a solution

Since the bar is in static equilibrium, both the net force and the net moment (torque) on the bar is 0.

Force N is the normal force that the wall exerts on the bar, R is the reaction of the pivot, W is the weight of the bar and A is due to Archimedes's principle (a body immersed in a fluid experiences a buoyant force equal to the weight of the displaced fluid.)

N = 0
R + A - W = 0

(Point A is used as the torque's point of origin)

And this is where I get stuck.
Any help would be appreciated, thanks. :)