Subjective Type

Give the magnitude and direction of the net force acting on a stone of mass $$0.1$$ $$kg$$.(a) Just after it is dropped from the window of a stationary train.(b) Just after it is dropped from the window of a train running at a constant velocity of $$36$$ $$km/h$$.(c) Just after it is dropped from the window of a train accelerating with $$1$$ $$m s^{-2}$$.(d) Lying on the floor of a train which is accelerating with $$1$$ $$m s^{-2}$$, the stone being at rest relative to the train. Neglect air resistance throughout

Solution

(a) Here, m = 0.1 Kg,
$$a=g=10 m/s^2$$
Net force, $$F = ma = 1 N$$
This force acts vertically downwards.
(b) When the train is running at a constant velocity, its acceleration $$= 0$$, No force acts on the stone due to this motion.
Therefore, force on the stone $$F =$$ weight of stone$$= mg= 0.1 \times 10 = 1.0 N$$
This force also acts vertically downwards.

(c) When the train is accelerating with 1 $$m/s^2$$,
an additional force $$ F' = ma = 0.1\times 1 = 0.1 N$$ acts on the stone in the horizontal direction.
But once the stone is dropped from the train,
F' becomes zero and the net force on the stone is $$F = mg = 0.1 $$\times $$ 10 = 1.0 N$$, acting vertically downwards.

(d) As the stone is lying on the floor of the train, its acceleration is the same as that of the train.
force acting on stone, $$F = ma = 0.1 \times 1 = 0.1 N$$
This force is along the horizontal direction of motion of the train.
Note that in each case, the weight of the stone is being balanced by the normal reaction.

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