Pivoting beam supported by a spring - equilibrium

1. Apr 11, 2010

Nihuepana

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

I have the following setup

http://yfrog.com/f1opgave4j

The beam turns without friction around the pivot support and is supported by a vertical, massless spring. When in equilibrium the spring is compressed by the the length b.

My target variables are the spring constant, k and the forces from the support on the beam during equilibrium.

2. Relevant equations

I state that the beam is at an angle,$$\theta$$ with horizontal.
I suppose that the system is in a static equilibrium and I'm using the second equilibrium condition.

3. The attempt at a solution

I find my angle
$$\theta=\arcsin \left( {\frac {b}{L}} \right)$$

First off I have my second equilibrium condition

$$F_{{{\it elastiv},{\it vertical}}}\cos \left( \theta \right) L+1/2\,W \cos \left( \theta \right) L+F_{{{\it elastic},{\it horizontal}}}b=0$$

I can see that the spring necessarily must follow the end of the beam in the x direction, which is why I conclude that it attacks the end of the beam with a force in the x direction that will have it's opposite counterpart at the pivot.

I'm also pretty sure that if there had been no deflection in the direction for the spring, then the force would have been -k*b and I could easily have found k. As it is I have no idea how the spring will act when it bends or how to get further on with the problem in general, so I really hope you guys can help me.

Best,
Simon

P.S
The image won't show unless it's opened in a new tab - must be doing something wrong :(

Last edited: Apr 11, 2010