ANSWER
a) FL = 2893.95 N
b) FR = 1324.35 N
EXPLANATION
The beam has a mass of 110 kg, so even before the piano is placed the ends of the beam support and initial force. The gravitational force (or weight) of the beam is:
[tex]\begin{gathered} Fg=m\cdot g=110\operatorname{kg}\cdot9.81\frac{m}{s^2} \\ Fg=1079.1N \end{gathered}[/tex]This is the total weight of the beam. Each end is under half this force:
[tex]F_{support}=\frac{Fg}{2}=539.55N[/tex]Now we add the piano. Let's make a diagram to see the situation better:
The piano has a mass of 320kg. Its total weight is:
[tex]Fg_{piano}=m_{piano}\cdot g=320\cdot9.81=3139.2N[/tex]Since the piano is not at the middle of the beam, each end will not support the same weight.
The additional weight on the left support is:
[tex]F_{\text{Lextra}}=\frac{3}{4}\cdot Fg_{piano}=2354.4N_{}[/tex]So the total force on the left support is:
[tex]F_L=2354.4N+539.55N=2893.95N[/tex]In the same way, the rest of the piano's weight is supported by the right support:
[tex]F_{\text{Rextra}}=\frac{1}{4}Fg_{piano}=784.8N[/tex]And the total force supported by the right support is:
[tex]F_R=784.8N+539.55N=1324.35N[/tex]
