Question

A 175 kg horizontal beam is supported at each end. A 310 kg piano rests a third of the way from one end.

What is the vertical force on the support closest to the piano?
N
What is the vertical force on the support furthest from the piano?
  N

Answer 1

under equilibrium condition

sum of upward force is equal to sum of down ward forces

F1 + F2 = W1 + W2

F1 +F2 = ( 175+310) 9.8)= 4753 N

clock wise moment of force F1 = counterclockwise moment of F2

W2 ( L/2) + W1 ( L/2) = F2L

W2/3 + W1/2 = F2

vertical force on the right support

F2 = 310(9.8)/ 3 + 175(9.8)/2

=1012.6 + 857.5 N

= 1870.16 N

left support F1 = 4753 N - 1870.16 N = 2879.3 N

the vertical force on the support closest to the piano is 2879.3 N

the vertical force on the support furthest from the piano is 1870.16 N