Question

A 20 kg, 10 m long aluminum painter’s plank is supported by a cable at each end. When the painter is standing somewhere on the plank, the left cable exerts a force of 400 N and the right cable exerts a force of 600 N. Determine the mass and location of the painter standing on the plank. What assumptions did you make? Main focus should be conceptually deriving the Equations and less focus on numerically solving equation.

Answer 1

here,

let the force mass and location of the painter is m and x from the left end

Now, balancing the forces in vertical direction

as there is no acceleration in the vertical direction

400 + 600 - m * g - 20 * h = 0

m * 9.8 = 1000 - 20 * 9.8

m = 82 Kg

the mass of the painter is 82 Kg

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balancing the torque about the left end

600 * 10 - 20 * 9.8 * 10/2 - 82 * 9.8 * x = 0

solving for x

x = 6.25 m

the location of the painter is 6.25 m from the left end