Question

An $8000kg$ 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 (c)the force of wagon $1$ on wagon $2$.

Answer 1

Step 1: Given Data

The mass of the engine $M=8000kg$

Total number of wagons $n=5$

Mass of each wagon $m=2000kg$

Force exerted by the engine $F=40000N$

The frictional force of the tracks $f=5000N$

Step 2: Calculate the net force

Therefore the net accelerating force on the train can be given as

$F_{net}=F-f$

$=40000-5000$

$=35000N$

Step 3: Acceleration of the train

The total mass of the train can be given as

$m_t=M+nm$

$=8000+5\times 2000$

$=18000kg$

Let the acceleration of the train be $a$.

The net force can be given as

$F_{net}=m_{t}a$

$\Rightarrow a=\frac{F_{net}}{m_t}$

$\Rightarrow a=\frac{35000}{18000}$

$\Rightarrow a=1.944m/s^2$

Step 4: Force applied between wagon $1$ & $2$

The force applied to wagon $2$ by wagon $1$ can be given as

$F_{21}=4ma$

$=4\times 2000kg\times 1.944\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right.$

$=15552N$

Hence, (a) the net accelerating force is $35000N$ (b) the acceleration of the train is $1.944m/s^2$ (c) the force of wagon $1$ on wagon $2$ is $15552N$.