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 and
(b) the acceleration of the train.​

Answer 1

35000,1.944

Explanation:

Given parameters

Mass of the engine = 8000 kg

Number of wagons = 5

Mass of the wagons = 2000 kg

Force exerted by the engine (F ) = 40000 N

Frictional force offered by the track (Ff) = 5000 N

(a) Net accelerating force (Fa) = F – Ff

Fa = 40000 N – 5000 N

Fa = 35000 N

(b) Let us consider the acceleration of the train be a m/s2

Acceleration is the ratio of net acceleration force by mass, i.e

a = Fa/m

Where m is the mass of the train, it can be calculated as follows

Total mass of the train (m) = Mass of the engine + (Mass of the wagons + Number of wagons)

m = 8000 + (5 × 2000)

m = 18000 kg

Acceleration of the train (a) = 35000/18000

a = 1.944m/s2

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Answer 2

$\huge\star{\underline{\underline{\sf\pink{ Solution :-} }}}$

Given,

• Force exerted by the train (F) = 40,000 N
• Force of friction = -5000 N (negative sign indicatesforce in opposite direction)

To Find:

• The net accelerating force ?
• The acceleration of the train ?

SolutiOn:

1st Case:

Therefore,

The net accelerating force = Sum of all forces

$\\ \implies{\sf{ 40,000\:N + (-5000\:N) }}$

$\implies\sf{ 35,000 \: N}$

2nd Case:

$\bullet{\underbrace{\boxed{\sf\red{ Total\:mass_{(train)} = Mass\:of\: Engine + Mass\: of\:each\:wagon }} }}$

$\implies\sf{8000kg + 5 \times 2000kg}$

$\implies\sf{18000 \:kg}$

So,

The total mass of the train is 18000 kg.

As per the second law of motion,

$\huge\bullet{\boxed{\sf{F = m \times a}}}$

Therefore,

$\bullet{\boxed{\sf{ Acceleration\:of\:the\:train = \dfrac{Accelerating\:Force}{Total\:Mass} }}}$

$\implies{\sf{ \dfrac{35000}{18000} }}$

$\implies{\sf{ 1.94\: ms^{-2} }}$

Hence,

The acceleration of the train is ${\sf\pink{ 1.94\: ms^{-2} }} .$