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 frictional 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.

Explanation

(a) Calculation of the net accelerating force
Here, the force exerted by the engine is 40000 N and the opposing force of friction offered by the track is 5000 N.So,
Net accelerating force, F = Force of engine - Force of friction
=40000-5000
=35000 N
Thus, the net accelerating force (F) exerted by the engine is 35000 newtons. This force will be used in further calculations.
(b) Calculation of the acceleration of train
We have just calculated that the net force exerted by the engine on the train is 35000 N. Now, the mass of 1 wagon of train is 2000 kg, so the mass of 5 wagons of train will be `2000 xx 5`=10000 kg. In other words the mass of whole train is 10000 kg.
Now, Net force=mass of train`xx`acceleration
F=m`xx`a
So, 35000=10000`xx`a
And, `a=35000/10000ms^(-2)`
`a=3.5ms^(-2)`
Thus, the acceleration of the train is 3.5 `ms^(-2)`
(c) Calculation of force of wagon 1 on wagon 2
There are 5 wagons behind the engine (which have been marked 1, 2, 3, 4 and 5 in the Figure given

above) but there are only 4 wagons behind wagon 1. Now,
Force of wagon 1 on wagon 2=mass of 4 wagons (behined wagon 1)`xx`acceleration of train
`=200xx4xx3.5`
=28000N
Thus, the force of wagon 1 on wagon 2 is of 28000 newtons.