An 8000 kg engine pulls a train of 5 wagons, each of 2000 kg, along a horizontal track. If the engine exerts a force of 40000 N and the track offers a friction force of 5000 N, then calculate:

(a) the net accelerating force

(b) the acceleration of the train

(c) the force of wagon 1 on wagon 2.

(a) Given, force exerted by the train (F) = 40,000 N

Friction exerts a force of = -5000 N    {the negative sign indicates that the force is applied in the opposite direction}

\(\therefore \) The net accelerating force = sum of all forces = 40,000 + (-5000 ) = 35,000 N

(b) Total mass of the train = mass of engine + mass of each wagon = 8000 + 5 × 2000 = 18000 kg

We know that, F = ma \( \Rightarrow a = \frac{F}{m} \)

Therefore, acceleration of the train = (net accelerating force) / (total mass of the train)

\( \Rightarrow \frac{35,000}{18,000} = 1.94 m/s^2 \)

(c) Force of wagon 1 on 2 = mass of 4 wagons × acceleration

\( \Rightarrow F_{1,2} = 4 × 2000 × 1.94 \ \Rightarrow \ F = 1552 N \)