physics help?

Question

A 155 kg horizontal beam is supported at each end. A 290 kg piano rests a fifth 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 furthest from the piano?

Answer 1

The easiest way to solve this problem is to sum the torques around each end. The 155 kg beam has a weight of 155 x 9.8 N acting downward at its center. The sum of the torques about the end closest to the piano is L/2 x 155 x 9.8 + L/5 x 290 x 9.8 - F2 x L. Notice the length of the beam cancels out and F2 = 9.8 (155/2 + 290/5). F1 = 9.8(155/2 +4 x 290/5)

Hope this helps, Mike R

Answer 2

Let F=force at support furthest from piano.
F'=force at support closest to piano

Take torques at support closest to piano:

Clockwise torque=290g*L/5+155g*L/2
Counterclockwise torque=F*L

Clockwise torque=Counterclockwise torque
290g*L/5+155g*L/2=F*L

L cancels out.

568.4+759.5=F
F=1327.9N upward.

Sum up forces:

Upward forces=force at supports
=F+F'
Downward forces=155*g+290*g

Upward forces=Downward forces

F+F'=155*g+290*g
F'+1327.9 =1519+2842
F'=4361-1327.9
=3033.1N upward