A 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; and (c) the force of wagon 1 on wagon 2.

(a) 35000 N (b) 1.944 m/s2 (c) 15552 N

(a) Force exerted by the engine, F = 40000 N

Frictional force offered by the track, Ff = 5000 N

Net accelerating force, Fa = F Ff = 40000 – 5000 = 35000 N

Hence, the net accelerating force is 35000 N.

(b) Acceleration of the train = a

The engine exerts a force of 40000 N on all the five wagons.

Net accelerating force on the wagons, Fa = 35000 N

Mass of the wagons, m = Mass of a wagon × Number of wagons

Mass of a wagon = 2000 kg

Number of wagons = 5

m = 2000 × 5 = 10000 kg

Total mass (including the mass of engine), M = m + 8000 = 18000 kg

Fa = Ma

⇒ a = {F_a \over M} = {35000\over18000}

= 1.944 m/s2

(c) Mass of 4 wagons (excluding wagon 1) m = 2000 × 4 = 8000 kg

Acceleration of the train = 1.944 𝑚/𝑠2

∴ The force of wagon 1 on wagon 2 = 𝑚𝑎 = 8000 × 1.944 = 15552 N.

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