An electric locomotive moves a train with a mass of 1600 tons from its place.

An electric locomotive moves a train with a mass of 1600 tons from its place. With what acceleration does the train move if the drag coefficient is 0.005 and the traction force is 400 KN?

Given:

m = 1,600 tons = 1,600,000 kg = 1.6 * 10 ^ 6 kilograms – the mass of the electric locomotive;

k = 0.005 – resistance coefficient;

g = 10 m / s ^ 2 – free fall acceleration;

F = 400 kN = 0.4 * 10 ^ 6 Newton – traction force.

It is required to find the acceleration of the electric locomotive a (m / s ^ 2).

Let’s find the value of the friction force:

Ftr = k * N = k * m * g = 0.005 * 10 * 1.6 * 10 ^ 6 = 8 * 10 ^ 4 Newton.

Then the resultant force giving acceleration to the electric locomotive will be equal to:

F1 = F – Ftr = 0.4 * 10 ^ 6 – 8 * 10 ^ 4 = 40 * 10 ^ 4 – 8 * 10 ^ 4 = 36 * 10 ^ 4 Newton.

a = F1 / m = 36 * 10 ^ 4 / 1.6 * 10 ^ 6 = 0.36 * 10 ^ 6 / 1.6 * 10 ^ 6 = 0.36 / 1.6 = 0.225 m / s ^ 2 …

Answer: the train is moving with an acceleration of 0.225 m / s ^ 2.