Calculate force acting on rod to holding it stable.

[sareba]

Homework Statement

A uniform rod AB of weight 20N is hinged at a fixed point A. A force acts at B holding it in equilibrium at 30 degrees to the vertical through A. calculate force acting at B if it is perpendicular to the rod.

The Attempt at a Solution

I figured that the angle between the weight of the rod and the force on B is 60 degrees but i can't seem to find the angle between the weight and the normal reaction force at the hinge...

 

[tiny-tim]

hi sareba!

I figured that the angle between the weight of the rod and the force on B is 60 degrees but i can't seem to find the angle between the weight and the normal reaction force at the hinge...

easy …

there's only three forces on the rod, and so they must all go through the same point (why? ),

so just draw the reaction force (it's not the normal reaction force, btw) so that it goes through the point where the other two forces meet

 

[sareba]

Thanks for the quick reply!
Yes. I did that. If the forces are in equilibrium they should meet at one point. But still I can't calculate the answer with just one force and one angle known... I am sure i am overlooking something... Here is a diagram i came up with... I need to find one of the angles with a question mark on them...

 

[tiny-tim]

Thanks for the quick reply!
Yes. I did that. If the forces are in equilibrium they should meet at one point. But still I can't calculate the answer with just one force and one angle known... I am sure i am overlooking something... Here is a diagram i came up with... I need to find one of the angles with a question mark on them...

ah yes, that's exactly the right diagram

ok, call that bottom point C, and the length of the rod 2L …

you want to find angle GCA

you know the length of GA, and the angle CGA, and you can easily find the length of GC

then find the length of AC, and then the angle GCA

 

[sareba]

I am sorry. I didnt quite follow you. How do i know the length of GA? Do you mean GC?

 

[tiny-tim]

GA = L, half the length of the rod