Question

A 75kg painter stands on a 6m long uniform plank resting on a scaffold. If the plank's mass is 25kg , how close to the left end of the plank can he stand without tipping the plank? ( The scaffold supports are 3m apart, and the plank extends beyond the scafold supports, 1.5m on each end.)

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Mass of the plank = m = 25 kg

Mass of the painter = M = 75 kg

Length of the plank = L = 6 m

Distance of the scaffolds from each end of the plank = D = 1.5 m

Distance of the painter from the left end of the plank = X

Distance of the painter from the left scaffold = D₁ = D - X = 1.5 - X

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

Distance of the center of gravity of the plank from the left scaffold = D₂

D₂ = L/2 - D

D₂ = 6/2 - 1.5

D₂ = 1.5 m

The plank is just about to be tipped therefore the right side scaffold will exert no force on the plank.

Taking moment balance about the left scaffold,

X = 1 m

Distance from the left end of the plank the painter can stand without tipping the plank = 1 m