A 2.0-m-long rod has a density in kilograms per meter and x is the distance from the left end of the rod. The rod rests horizontally with each end supported by a scale. The force exerted by the left scales is

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A 2.0-m long rod has a density in kilograms per meters λ = a + bx, where a=1.0kg/m, b=1.0kg/m2, and x is the distance from the left end of the rod. The rod rests horizontally with each end supported by a scale. The force exerted by the left scale is?

answer : 13.08 N

Explanation:

Determine the force exerted by the left scale

Length of rod = 2.0 m

Density of rod ( λ )= a + bx = 1 + 1x

First step ; Determine the moment

∑ moment = 0 =  F * 2 - (( 1 * 2 * g * 2/2) + (1/2 * 2 * 1 * g * (2/3 ) )

∴ F = 4g / 3

     = 4 * 9.81 / 3 =  39.24 / 3 = 13.08 N