Question

Two scales sit on the ground a distance of 4.0m apart. A 6.0m long plank of mass 10.0kg is supported by the scales. The plank extends 1.0m past each scale. Frito and Fungo ( each weighs 50.0N ) sit on the plank. Frito sits 1.0m to the left of the right hand scale and Fungo sits 1.0m to the right of the same scale. What is the reading on the right hand scale?

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Mass of the plank = M = 10 kg

Weight of Frito = W₁ = 50 N

Weight of Fungo = W₂ = 50 N

Length of the plank = L = 6 m

Reading on the left hand scale = N₁

Reading on the right hand scale = N₂

Distance between the two scales = D = 4 m

Distance of Frito from the left hand scale = D₁ = 4 - 1 m = 3 m

Distance of Fungo from the left hand scale = D₂ = 4 + 1 m = 5 m

The center of gravity of the plank will lie at the midpoint of the plank.

Distance of the center of gravity of the plank from the left hand scale = D₃ = 3 - 1 m = 2 m

Taking moment balance about the left hand scale,

W₁D₁ + W₂D₂ + MgD₃ = N₂D

(50)(3) + (50)(5) + (10)(9.81)(2) = N₂(4)

N₂ = 149.05 N

Reading on the right hand scale = 149.05 N