A 160kg horizontal beam is supported at each end. A 330kg piano rests a quarter of the way from one end.

Question

What is the vertical force on each of the supports?

Answer 1

I'll choose to place the piano 1/4 way from the right end

Fr= force right
Fl=force left

Fr+Fl-W-mg=0 where mg is the weight of the beam, W is the weight of the piano
(The sum of the forces in the vertical direction is zero because nothing is moving)

Then sum of the torques about any point will also be zero, because the beam is stationary. The weight of the beam acts halfway down the plank. The torque about the right end:

W*L/4+mgL/2-Fl*L=0
solve for Fl, then use Fr+Fl-W-mg=0 to solve for Fr

Answer 2

Fr=5N