How Do You Calculate Vertical Forces on Beam Supports with a Piano?

[kp87]

Homework Statement

A 75.0 kg horizontal beam is supported at each end. A 275 kg piano rests a quarter of the way from one end. What is the vertical force on the support closest to the piano?
What is the vertical force on the support farthest from the piano?

Homework Equations

Tcw=Tccw

The Attempt at a Solution

I tried using Tcw=Tccw
so Fpiano*r1+Fbeam*r2=Fbeam*r3
so 275*9.81*3/4+75*9.81*1/2=Fb*1
So I got 2391N for the farthest beam
and 275*9.81*1/4+75*9.81*1/2=Fb*1
and got 1042N for the closer one but they seem to be wrong...
can you guys help me on this?

nvm... I got the answer now I did it backwards so the one with 1042N is farthest and 2391N is the closest...
thanks lol

 

[radou]

Simplify your notation. Let A be the reaction force at the support closer to the piano (let's say, the left one), and B the other reaction force. Then set the sum of moments around support B (the one further from the piano) equal to zero. Let the length of the beam be L.

Edit: don't forget to count the weight of the beam (whose resultant is acting at the center of the beam) in your calculation.