Question

A 8000kg engine pulls a train of 5 wagons, each of 2000kg, along a horizontal track. If the engine exerts a force of 40000N and the track offers a friction force of 5000N, then calculate:
(a) the net accelerating force;
(b) the acceleration of the train; and
(c) the force of wagon 1 on wagon 2.

Answer 1

Given, force of engine = 40000 N

Force of friction = 5000 N

Mass of engine = 8000 kg

Total weight of wagons = 5 x 2000 kg = 10000 kg

(a) The net accelerating force

= Force exerted by engine – Force of fricition

= 40000 N – 5000 N = 35000 N

b) The acceleration of the train

We know that, F = mass x acceleration

Or, 35000 N = (mass of engine + mass of 5 wagons) X a

Or, 35000 N = (8000 kg + 10000 kg) X a

Or, 35000N = 18000 kg X a

⇒a=35000N18000kg=1.944ms−2⇒a=35000N18000kg=1.944ms-2

(c) The force of wagon 1 on wagon 2

Since, net accelerating force = 35000 N

Mass of all 5 wagons = 10000 kg

We know that, F = m x a

Therefore, 35000N = 10000 kg x a

⇒a=35000N10000kg=3.5ms−2⇒a=35000N10000kg=3.5ms-2

Therefore, acceleration of wagons=3.5m/s2=3.5m/s2

Thus, force of wagon 1 on 2 = mass of four wagons x acceleration

⇒F=4×2000kg×3.5ms−2

F=8000kg×3.5ms−2⇒F=8000kg×3.5ms-2

⇒F=28000N⇒F=28000N

Thus, (a) The net accelerating force = 35000N

(b) The acceleration of train = 1.944 ms^–2

(c) The force of wagon 1 on 2 = 28000N