Newton’s Second Law of Motion

NEWTON’S SECOND LAW OF MOTION

According to this law, “the force acting on a body is directly proportional to the rate of change of linear momentum of the body and the change in momentum takes place in the direction of the force”.

This law helps us to measure the amount of force. So, it is also called as ‘law of force’. Let, ‘m’ be the mass of a moving body, moving along a straight line with an initial speed ‘u’ After a time interval of ‘t’, the velocity of the body changes to ‘v’ due to the impact of an unbalanced external force F.

Initial momentum of the body P_i = mu

Final momentum of the body P_f = mv

Change in momentum Δp = P_f –P_i

= mv – mu

By Newton’s second law of motion,

Force, F ∝ rate of change of momentum

F ∝ change in momentum / time

Here, k is the proportionality constant. k = 1 in all systems of units. Hence,

Since, acceleration = change in velocity/ time, a=(v-u)/t. Hence, we have

F = m × a (1.6)

Force = mass × acceleration

No external force is required to maintain the motion of a body moving with uniform velocity. When the net force acting on a body is not equal to zero, then definitely the velocity of the body will change. Thus, change in momentum takes place in the direction of the force. The change may take place either in magnitude or in direction or in both.

Force is required to produce the acceleration of a body. In a uniform circular motion, even though the speed (magnitude of velocity) remains constant, the direction of the velocity changes at every point on the circular path. So, the acceleration is produced along the radius called as centripetal acceleration. The force, which produces this acceleration is called as centripetal force, about which you have learnt in class IX.

Units of force: SI unit of force is newton (N) and in C.G.S system its unit is dyne.

Definition of 1 newton (N): The amount of force required for a body of mass 1 kg produces an acceleration of 1 m s^–2, 1 N = 1 kg m s^–2

Definition of        1 dyne: The amount of force required for a body of mass 1 gram produces an acceleration of 1 cm s^–2, 1 dyne = 1 g cm s^–2; also 1 N = 10⁵ dyne.

Unit force:

The amount of force required to produce an acceleration of 1 m s^–2 in a body of mass kg is called ‘unit force’.

Gravitational unit of force:

In the SI system of units, gravitational unit of force is kilogram force, represented by kg f. In the CGS system its unit is gram force, represented by g f.

1 kg f = 1 kg × 9.8 m s^-2 = 9.8 N;

1 g f = 1 g × 980 cm s^-2 = 980 dyne