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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 $$5000N$$ then calculate
a) the net accelerating force.
b) the acceleration of the train and
c) the force of wagon $$1$$ on wagon $$2$$.


Solution

a) Net accelerating force = Force exerted by engine – Frictional force.
(Here the frictional force is subtracted because it opposes the motion)
$$= 40000 – 5000 = 35000 N$$
$$= 3.5 \times  104 N$$.
b) From Newton’s second law of motion,
Accelerating force = mass of the train * Acceleration of train,
$$a = \dfrac{F}{m}$$
Mass of train = Mass of engine + Mass of all wagons,
$$= 8000 + 5 \times  2000$$
$$= 8000 + 10000$$
$$= 18000 Kg$$.
$$\therefore$$ Acceleration $$=\dfrac{35000}{18000}=\dfrac{35}{18}$$
$$= 1.95 ms^{-2}$$.
c) Force of wagon $$1$$ on wagon $$2$$
= Mass of the engine * Acceleration,
$$= 800 \times  1.95 = 15600 N$$.

Physics

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