Question

Shows a uniform beam of mass m pivoted at its lower end, with a horizontal spring attached between its top eitd and a vertical wall. The beam makes an angle 6 with the horizontal. Find expressions for (a) the distance (I the spring is stretched from equilibrium and the components of the force exerted by the pivot on the beam.

Answer 1

The arrangement shown is in static equilibrium.
If the spring is stretched by d, the force on the spring is kd
Take L as the length of the beam
a)
Equating the torque about the pivot,
L/2 x mgcos $\theta$ = L x kd sin $\theta$
d = mg cot $\theta$ / 2k

b)
Take the force exerted by the pivot be Fx and Fy
If we now equate the forces,
Fx = kd = 0.5 mg cot $\theta$
Fy = mg