What is the rigidity of the towing cable if, when towing a car weighing 2 tons, the cable lengthened by 2 mm

What is the rigidity of the towing cable if, when towing a car weighing 2 tons, the cable lengthened by 2 mm, and the car reached a speed of 2 m / s after 4 seconds after the start of movement? The friction coefficient is considered equal to 0.1, and the movement is uniformly accelerated.

m = 2 t = 2000 kg.

g = 10 N / kg.

Δl = 2 mm = 0.002 m.

V0 = 0 m / s.

V = 2 m / s.

t = 4 s.

μ = 0.1.

k -?

m * a = Ft + Ftr + N + m * g – 2 Newton’s law in vector form.

ОХ: m * a = Fт – Fтр.

OU: o = N – m * g.

a = (V – V0) / t.

Ftr = μ * N = μ * m * g.

Ft = Fcont = k * Δl.

m * (V – V0) / t = k * Δl – μ * m * g.

k * Δl = m * (V – V0) / t + μ * m * g.

k = m * (V – V0) / t * Δl + μ * m * g / Δl.

k = 2000 kg * (2 m / s – 0 m / s) / 4 s * 0.002 s + 0.1 * 2000 kg * 10 N / kg / 0.002 s = 3 000 000 N / m = 3 * 106 N / m = 3 MN / m.

Answer: the stiffness of the towing cable of the car is k = 3,000,000 N / m.