A car with a mass of 20 tons moves along a horizontal section of the track at a speed of 5 ms, automatically

| March 13, 2021 | education

A car with a mass of 20 tons moves along a horizontal section of the track at a speed of 5 ms, automatically on the move, it clings to stationary cars of a mass of 10 tons. Determine the braking time of the cars if the braking distance is 20m.

m1 = 20 t = 20,000 kg.

V1 = 5 m / s.

V2 = 0 m / s.

m2 = 10 t = 10000 kg.

S = 20 m.

V = 0 m / s.

t -?

Let us find the speed of the cars immediately after the coupling V “according to the law of conservation of momentum.

m1 * V1 + m2 * V2 = (m1 + m2) * V “.

V “= (m1 * V1 + m2 * V2) / (m1 + m2).

V “= (20,000 kg * 5 m / s + 10,000 kg * 0 m / s) / (20,000 kg + 10,000 kg) = 3.3 m / s.

We will assume that the cars were moving uniformly when braking.

a = (V “2 – V ^ 2) / 2 * S = V” 2/2 * S.

a = (V “- V) / t = V” / t.

V “2/2 * S = V” / t.

t = 2 * S / V “.

t = 2 * 20 m / 3.3 m / s = 12.1 s.

Answer: the braking of the cars lasted t = 12.1 s.



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