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: (a) the net accelerating force (b) the acceleration of the train (c)the force of wagon 1 on wagon 2.

Answer 1

Explanation :-

Given :

Force of the engine,f = 40000N

Force of friction,F = 5000N

Mass of the engine,m = 8000kg

To Find :

Net accelerating force, the acceleration of the train and the force of wagon 1 on wagon 2.

Solution :

a)The net accelerating force = Force exerted by engine - Force of friction.

⇒ 40000N - 5000N

∴ 35000N

b)We know that F = m × a, where f is the force applied ,m is the mass of the body and a is the acceleration.

So,

$\sf{}\implies 35000N=(mass\ of \ the\ engine + mass\ of\ 5\ wagons) \times a$

$\sf{}\implies35000N=(8000kg + 10000kg) \times a$

$\sf{}\implies35000N=18000kg \times a$

$\sf{}\implies\dfrac{35000N}{18000kg}= a$

$\sf{}\therefore a= 1.944ms^{-2}$

c)Net accelerating force = 35000

Mass of all 5 wagons = 10000kg

We know that, F = ma

Therefore,

$\sf{}\implies 35000N = 10000kg \times a$

$\sf{}\implies \dfrac{35000N}{10000kg}=a$

$\sf{}\therefore a=3.5ms^{-2}$

Therefore,acceleration of the wagons = 3.5ms^-2

Thus,force of the wagon 1 on 2 = Mass of four wagons  acceleration

$\sf{} \implies F = 4\times 2000kg \times 3.5ms^{-2}$

$\sf{} \implies F = 8000kg \times 3.5ms^{-2}$

$\sf{} \therefore F = 28000N$

Thus,

a) The net accelerating of the force = 35000N

b) The accelerating of the train = 1.944ms^-2

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