Find Equilibrium: Solving a Uniform Bar Problem

[snshusat161]

Homework Statement

A uniform bar AB of length l and weight W is hinged to the wall at its end A and supported by means of a string of length a which is tied to the wall as shown. Find the angle \theta that the bar will make with the wall corresponding to the position of equilibrium

Homework Equations

Moment = Force X perpendicular distance

The Attempt at a Solution

I had tried to find moment about point A. I had resolved W and T (tension in the string BC) into rectangular components. One along the bar and other perpendicular to the bar. along the bar components will not add to the moments at A while the perpendicular components will get multiplied by the distance (For T and W, l and l/2 respectively) and added according to sign convention (anticlock wise rotation as positive and clockwise rotation as negative). but because the angle ABC is getting too bulky (complicated), I don't think I can anyhow end this problem with answer. Need your immediate help.

 

[snshusat161]

More info:

W acts from the center of the bar.

angle A = \theta

 

[pongo38]

Are you sure there isn't another bit of information?

 

[snshusat161]

very sure!

 

[zhermes]

There isn't enough information to solve the problem. You need to know where 'C' is.

 

[pongo38]

In the diagram attached (I hope it does) it shows the 3 forces W RA and RC meeting at the midpoint of the string. The two triangles (G for geometry, and F for forces) should be similar, and there should be enough information to conclude all the dimensions and forces. The only dimension not shown is the horizontal projection of the G triangle, and that is L/2*(cos theta). But there still is not enough information to bring this to completion.

 

[MIGOM PEGU]

I want the solutions of all the problem i.e in this chapter. So please help me in solving the problem of this chapter...