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.

#### Solution

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

Frictional force offered by the track, *F*_{f} = 5000 N

Net accelerating force, *F*_{a} = *F* − *F*_{f} = 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, *F*_{a} = 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, M = *m* = 10000 kg

From Newton’s second law of motion:

F_{a} = *Ma*

`a=F_a/m`

`=35000/10000`

`=3.5"ms"^-2`

Hence, the acceleration of the wagons and the train is 3.5 m/s^{2}.

(c)Mass of all the wagons except wagon 1 is 4 × 2000 = 8000 kg

Acceleration of the wagons = 3.5 m/s^{2}

Thus, force exerted on all the wagons except wagon 1

= 8000 × 3.5 = 28000 N

Therefore, the force exerted by wagon 1 on the remaining four wagons is 28000 N.

Hence, the force exerted by wagon 1 on wagon 2 is 28000 N.