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)force= mg = 0.1x10=1N

(vertically downwards)
the train is stationary so the net force acting on the stone is the force of gravity .
b)force=mg=0.1x10=1N
(vertically downwards)

the train moves with a constant velocity so no acceleration and no force acts in the horizontal direction.

c)force= mg=0.1x10=1N
(vertically downwards)
although a force of 0.1N acts on the stone in the horizontal position the force does not act on the stone at the instance when it is dropped.

d)force=mg=0.1x1=0.1N
(horizontal direction)

Answer 2

(a)1 N; vertically downward

Mass of the stone, m = 0.1 kg

Acceleration of the stone, a = g = 10 m/s2

As per Newton’s second law of motion, the net force acting on the stone,

F = ma = mg

= 0.1 × 10 = 1 N

Acceleration due to gravity always acts in the downward direction.

(b)1 N; vertically downward

The train is moving with a constant velocity. Hence, its acceleration is zero in the direction of its motion, i.e., in the horizontal direction. Hence, no force is acting on the stone in the horizontal direction.

The net force acting on the stone is because of acceleration due to gravity and it always acts vertically downward. The magnitude of this force is 1 N.