A uniform smooth plank weight W and lenght 2a is hinged to the bottom horizontal edge of a smooth, fixed plane inclined at angle (beta) to the horizontal. A sphere of radius (1/2)a and weight 2W is placed between the plank and the plane. Assume no friction. Prove that, in the position of equilibrium, the angle (theta) between the plank and the plane will be given by the equation
2sin^2(theta/2) * cos(theta + beta) = sin (beta)
sum of torque =0
sum of force along(x and y) = 0
The Attempt at a Solution
I try to draw a FBD, but i dont know where to start to get to that equation :x.
(the pic is drawn not to scale)