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

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To calculate the vertical forces on beam supports with a piano, the problem involves a 75 kg beam supported at both ends with a 275 kg piano placed a quarter of the way from one end. The correct approach is to set the sum of moments around the support farthest from the piano to zero, incorporating both the weight of the piano and the beam. Initially, incorrect calculations were made, but the correct forces were identified as 1042 N for the support farthest from the piano and 2391 N for the closest support. It is crucial to include the weight of the beam in the calculations for accurate results. Proper notation and moment calculations are essential for solving such problems effectively.
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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
 
Last edited:
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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.
 

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