Question

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

Answer 1

(a) Here, m = 0.1 Kg,

$a=g=10m/s^2$

Net force, $F=ma=1N$

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$=mg=0.1\times 10=1.0N$

This force also acts vertically downwards.

(c) When the train is accelerating with 1 $m/s^2$,

an additional force $F^{\prime }=ma=0.1\times 1=0.1N$ 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 $10=1.0N$, 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, $F=ma=0.1\times 1=0.1N$

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.