Calculate force acting on rod to holding it stable.

AI Thread Summary
A uniform rod AB weighing 20N is hinged at point A and held at a 30-degree angle to the vertical by a force at point B, which is perpendicular to the rod. The discussion revolves around calculating the force at B while considering the equilibrium of forces acting on the rod. Participants clarify that all forces must converge at a single point due to equilibrium conditions, and they discuss the geometry involved in determining the necessary angles and lengths. The challenge lies in finding the unknown angles and lengths to solve for the force at B. The conversation emphasizes the importance of understanding the relationships between the forces and the geometry of the setup.
sareba
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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...
 
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hi sareba! :smile:
sareba said:
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? :wink:),

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 :smile:
 
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...
 

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sareba said:
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 :smile:

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 :wink:
 
I am sorry. I didnt quite follow you. How do i know the length of GA? Do you mean GC?
 
GA = L, half the length of the rod
 
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