How long will a fishing line with a coefficient of elasticity of 0.5 kN / m

How long will a fishing line with a coefficient of elasticity of 0.5 kN / m lengthen when a fish weighing 250 g is lifted vertically upwards.

The elastic force that acts on the line is balanced by the force of gravity, which is created by the mass of the fish:

Fcont. = Fт.

Fcont. = k * ∆l, where k is the rigidity of the line (k = 0.5 kN / m = 500 N / m); ∆l – line extension.

Fт = m * g, where m is the mass of the caught fish (m = 250 g = 0.25 kg), g is the acceleration of gravity (we take g = 10 m / s²).

Let’s express and calculate the extension of the line:

k * ∆l = m * g.

∆l = m * g / k = 0.25 * 10/500 = 2.5/500 = 0.005 m = 5 mm.

Answer: Line elongation is 5 mm.