M2: moments when forces are not perpendicular

AI Thread Summary
In the discussion, a uniform rod pivoted at point A is analyzed for equilibrium conditions with a weight hanging from a string. It is established that the string must be perpendicular to the rod in equilibrium due to the balance of forces. The angle theta that the rod makes with the vertical is derived, showing that tan theta equals 4/3. Participants clarify the tension in the string, correcting initial misunderstandings about the forces involved. The conversation emphasizes the importance of accurately applying moment equations and understanding the relationships between the forces acting on the system.
pianogirl
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Homework Statement



A smooth uniform rod AB, of length 3a and weight 2w, is pivoted at A so that it can rotate in a vertical plane. A light ring is free to slide along the rod. A light inextensible string is attached to the ring and passes over a fixed smooth peg at a point C, a height 4a above A, and carries a particle of weight w hanging freely.
a) Give reasons why in equilibrium, the string will be at right angles to the rod.
b) show that the angle theta that the rod makes to the vertical in equilibrium is given by tan theta= 4/3
c) Find the magnitude of the force of the pivot on the rod A in terms of w.

Homework Equations



Moment stuff like M= Fd and in equil., total anticlockwise moments= total clockwise moments.

The Attempt at a Solution


Well, I drew a diagram.
For part b, I tried doing moments around A to get Tension in the string= 2w sin theta.
When I did sohcahtoa, I got tan theta= 4w sin theta/3a.

And basically, I'm confused.
Help would be appreciated!
Thanks!
 
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Hi pianogirl! :smile:
pianogirl said:
For part b, I tried doing moments around A to get Tension in the string= 2w sin theta.

How did you get this? :confused: The tension holding the weight w in equilibrium is just w.
 
Oh yeah! Totally forgot that. Thanks! Will try again!
 

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