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 and (b) the acceleration of the train.

Given parameters

Mass of the engine (M) = 8000 kg

Number of wagons = 5

Mass of the wagons (m) = 2000 kg

Force exerted by the engine (F ) = 40000 N

Frictional force offered by the track (Ff) = 5000 N

(a) Net force (Fa) = F – Ff

Fa = 40000 N – 5000 N

Fa = 35000 N

(b) Let us consider the acceleration of the train to be a m/s2

Acceleration is the ratio of net acceleration force by mass, i.e.

a = Fa/m

Where m is the mass of the train, it can be calculated as follows

The total mass of the train (m) = Mass of the engine + (Mass of the wagons  × Number of wagons)

m = 8000 + (5 × 2000)

m = 18000 kg

Acceleration of the train (a) = 35000/18000

a = 1.944m/s2

(c) F21 = m4w × a

• F21 = Force applied on Wagon 2 by Wagon 1
• m4w = mass of 4 wagons
• a = acceleration of the train

The force of wagon 1 on wagon 2 = Force of wagon 2 on wagon 1

⇒ (4 × 2000 × 1.944)

= 15552 N

The force of wagon-1 on the wagon-2 is 15552 N.