let the length of the beam be "L"
from the diagram
AD = length of beam = L
AC = CD = AD/2 = L/2
BC = AC - AB = (L/2) - 1.10
BD = AD - AB = L - 1.10
m = mass of beam = 20 kg
m₁ = mass of child on left end = 30 kg
m₂ = mass of child on right end = 40 kg
using equilibrium of torque about B
(m₁ g) (AB) = (mg) (BC) + (m₂ g) (BD)
30 (1.10) = (20) ((L/2) - 1.10) + (40) (L - 1.10)
L = 1.98 m
The total length of the beam is determined as 1.98 m.
The length of the beam is determined by applying the principle of moment as shown below;
Take moment about the pivot;
Let the total length of the beam = x
mid point of the beam = 0.5 x
(30 x 1.1) = 20(0.5x - 1.1) + 40(x - 1.1)
33 = 10x - 22 + 40x - 44
99 = 50x
x = 99/50
x = 1.98 m
Thus, the total length of the beam is determined as 1.98 m.
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