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.

Answer

(a) 35000 N
(b) 1.944 `m S^(-2)` ( c)15552 N

Explanation

(a) Force exerted by the engine , F=40000 N
Frictional force offered by the track, `F_(f)=5000N`
Net accelerating force, `F_(a)=F-F_(f)=40000-5000=35000 N`
Hence, the net accelerating force is 35000 N.
(b) Accelerating 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 wagon, m= Mass of a wagon `xx` Number of wagons
Mass of wagon=2000 kg
Number of wagon = 5
`:. m=2000xx5=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 wagon and the train is `3.5m//s^(2)`.
(c) Mass of all the wagons except wagon 1 is `4xx2000=8000 kg`
Acceleration of the wagons = `3.5 m//s^(2)`
Thus, force exerted on all the wagons except wagon 1 =`8000xx3.5=28000 N`
Therefore, the force exerted by wagon 1 on the remaining four wagon is 28000 N.
Hence, the force exerted by wagon 1 on wagon 2 is 28000 N.