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 = Fa / ma = 35000 / 18000 = 1.944 m/s 2
(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 = = 8000 × 1.944 = 15552 N