Q. 34.1( 46 Votes )

# 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 :

According to the Newton’s second law of motion:

F = m × a

Where,

‘F’ is the magnitude of the force acting on an object.

‘m’ is the mass of the object.

‘a’ is the acceleration of the object.

Given,

Mass of the stone, m = 0.1 kg

Acceleration due to gravity is taken as ‘g’ = 10 m/s^{2}

A. When the train is stationary the net force acting on it is only due to gravitational force. Thus, the magnitude of the force is

F= m×a = m×g

=0.1 kg×10 m/s^{2}

F = 1 N

Therefore, the net force acting on the stone will be due to gravitation which is always in the downward direction.

B. When the train is moving with a constant velocity. The rate of change of velocity i.e. acceleration is zero. Thus, there is no net force acting on the stone in the horizontal direction.

The only force that acts is in vertical direction i.e. gravitational force with the magnitude,

F= m×a= m×g

= 0.1 kg × 10 m/s^{2}

F = 1 N

Therefore, the net force acting on the stone is of the magnitude 1 N acting in the vertically downward direction.

C. When the stone leaves the train, the net force acting on it just after it has left does not consist of horizontal force as the force due to train stops acting on it the instant it leaves the train. According to Newton’s first law of motion, the force acting on a body at an instant depends on that instant.

The net force acting on the stone is given only by acceleration due to gravity.

F= m×a= m×g

= 0.1 kg × 10 m/s^{2}

F = 1 N acting in the downward direction.

Therefore, the net force acting on the stone is of the magnitude 1 N acting in the vertically downward direction.

D. Given,

Acceleration of the train,‘a’ = 1 m/s^{2}

When the stone is lying on the floor of the train the weight of the stone is balanced by the normal reaction of the floor. The vertical forces vanish and only the horizontal force remains which is due to the acceleration of the train.

Thus the net force acting on the stone will be in the same direction as the train,

The magnitude of the net force is,

F= ma

⇒ F=0.1 m/s^{2} × 1 kg = 0.1 N

Therefore, the net force acting on the stone is of the magnitude 1 N acting in the same direction as the train.

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