A sturdy wooden plank, 4.0 meters long and with a mass of 42 kg, rests on two su
ID: 2199028 • Letter: A
Question
A sturdy wooden plank, 4.0 meters long and with a mass of 42 kg, rests on two supports (labeled L and R) placed 1.2 m from each end. The figure should look something like this.
(a) Suppose that a man with a mass of 72 kg stands at the center of the board (point a). What are the upward forces on the board from each support?
(b) Now the man stands 1.0 m from one end of the board (point b). What are the upward forces from each support now?
(c) The man edges gradually toward the end of the board. At what distance from the end does the board finally tip?
Explanation / Answer
a)
W man = 72*9.8 = 705.6
W board = 411.6
M at L = -705.6*0.8 -0.8*411.6 + 1.6*R = 0
R = 558.6 N
M at R = 705.6*0.8 + 0.8*411.6 - 1.6*L = 0
L = 558.6N
b)
M at L = -705.6*1.8 -0.8*411.6 + 1.6*R = 0
R = 999.6N
M at R = -705.6*0.2 + 0.8*411.6 - 1.6*L = 0
L = 117.6N
c) M at R = 0.8*411.6 - 705.6x = 0
x = 0.47m from R
1.2-.47 = 0.73m from the edge
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