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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 $5000 N$ , The force between of wagon $1$ on the wagon $2$ is[[1]]N.

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Detailed Solution

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

, The force between of wagon

1

on wagon

2

15552 N .

Given that,
Mass [9][10]of each wagon (m)

= 2000 kg

Number of wagons

n = 5

Mass of the engine

M = 8000 kg

The effort made by the engine

F = 40000 N

The frictional force of the tracks

f = 5000 N

Step 1, Net Force:
Consequently, the train's net accelerating force can be expressed as
⇒

F_{net} = F - f

⇒

F_{net} = 40000 - 5000

⇒

F_{net} = 5000 N

Step 2, Acceleration of train:
The mass of the train as a whole can be expressed as
⇒

m_{t} = M + nm

⇒

m_{t} = 8000 + 5 ✕ 2000

= 18000 kg

Let the train's accelerating speed be

a .

The net force is expressed as

F_{net} = m_{t} ✕ a

⇒

a = F_{net} / m_{t}

\Rightarrow a = 35000 / 18000

⇒ Acceleration of the train

(a) = 1.94 m / s^{2}

Force applied between wagon 1 & 2
By using the formula of force

F = m \times a

\Rightarrow mass of 4 wagons \times acceleration of train

\Rightarrow

2000 \times 4 \times \frac{35}{18}

\Rightarrow

15552 N

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