Question

Rigid objects in equilibrium

Answer 1

Two circular pipes are fixed with their axes horizontal and parallel to each other. A uniform plank AB , of length 2 m and weight 162 N , rests on the pipes, with A higher than B, in a vertical plane which is perpendicular to the axes of the pipes (see diagram). The plank touches one of the pipes at X and the other at Y , where AX = 60 cm, XY= 70 cm and X is higher than Y .

The plank makes an angle of 30 degrees with the horizontal. Calculate the normal components of the contact forces on the plank at X and Y.

Answer 2

I have tried to work out the problem

First equation: Moment at A,
\[M(A) ~~~~~ n_x(60)-162\cos(60)(95) + n_y(130) =0\]
Sum of all forces parallel to rod, Equation 2,
\[n_x+n_y-162\cos(60)=0\]
\[n_x=81-n_y\]
\[n_x=40.5 N\]
The correct answer is 60.1 N and 80.2 N