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An $8000 kg$ 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 find the the acceleration of the train.

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3.5 m / s^{2}

7.0 m / s^{2}

5.5 m / s^{2}

3.2 m / s^{2}

answer is A.

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Detailed Solution

The acceleration of the train is

3.5 m / s^{2}

.
Given that each waggon weighs

2000 kg

and the engine weighs

M = 8000 kg

.
Force exerted by the engine,

F = 40000 N

Friction offers by the track,

f = 5000 N

Net accelerating force

=

Force exerted by the engine

-

Friction offered by the track
⇒

F_{a} = F - f

⇒

F_{a} = 40000 N - 5000 N

= 35000 N

Acceleration of the train,
By newton’s second law of motion, accelerating force is equal to product of mass and acceleration.
⇒

F_{a} = ma

⇒

a = \frac{F_{a}}{m}

⇒

a = \frac{35000}{10000}

⇒

a = 3.5 m / s^{2}

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