M2: moments when forces are not perpendicular

[pianogirl]

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!

 

[tiny-tim]

Hi pianogirl!

For part b, I tried doing moments around A to get Tension in the string= 2w sin theta.

How did you get this? The tension holding the weight w in equilibrium is just w.

 

[pianogirl]

Oh yeah! Totally forgot that. Thanks! Will try again!