Question

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:
$\left(a\right)$ The net accelerating force:
$\left(b\right)$ The acceleration of the train; and
$\left(c\right)$ The force of wagon $1$ on wagon $2$.

Answer 1

Given : Mass of engine $M=8000$ kg

Mass of each wagon $m=2000$ kg

Frictional force acting in backward direction $f=5000$ N

(a) : The net force acting on the train $F^{\prime }=F-f=40000-5000=35000$ N

(b) : Let the acceleration of the train be $a$

$\therefore$ $F^{\prime }=(5m+M)a$

$35000=(5\times 2000+8000)a$ $⟹a=1.944$ $m{s}^{-2}$

(c) : External force is applied directly to wagon 1 only. The net force on the last four wagons is equal to the force applied by wagon 2 by wagon 1.

Let the acceleration of the wagons be $a^{\prime }$

$35000=\left(5m\right)a^{\prime }$ $⟹35000=10000\times a^{\prime }$

Acceleration of the wagons $a^{\prime }=3.5$ $m{s}^{-2}$

Mass of last 4 wagons $m^{\prime }=4\times 2000$ kg

$\therefore$ Net force on last 4 wagons $F_1=8000\times 3.5$ $=28000$ N

Thus force on wagon 2 by wagon 1 is 28000 N.