The reaction force F₁ = 1500 N and the reaction force F₂ = 2500 N
Moment of a force
The moment of a force about a point, M is the product of the force F and its perpendicular distance from the point, d.
So, M = Fd
Considering the bridge, since it is in equilibrium, clockwise moments, M' = anticlockwise moments M".
The F₁ rection force
The reaction force F₁ = 1500 N
Taking moments about the F₂ force, we have
F₁ × 6 m = 1000 N × (6 m - 3 m) + 3000 N × (6m - 4 m)
F₁ × 6 m = 1000 N × 3 m+ 3000 N × 2 m
F₁ × 6 m = 3000 Nm + 6000 Nm
F₁ × 6 m = 9000 Nm
F₁ = 9000 Nm/6 m
F₁ = 1500 N
The reaction force F₁ = 1500 N
The F₂ reaction force
The reaction force F₂ = 2500 N
Taking moments about the F₁ force, we have
F₂ × 6 m = 1000 N × 3 m + 3000 N × 4 m
F₂ × 6 m = 3000 Nm + 12000 Nm
F₂ × 6 m = 15000 Nm
F₂ = 9000 Nm/6 m
F₂ = 2500 N
The reaction force F₁ = 1500 N and the reaction force F₂ = 2500 N
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