Newton’s second law of motion
When two bodies, a heavy one and a light one, are acted upon by the same force for the same time, the light body attains a higher velocity than the heavy one. But the momentum gained by both the bodies is the same. The link between force and momentum is expressed in Newton’s second law of motion.
According to Newton’s second law of motion:- The rate of change of momentum of a body is directly proportional to the applied force, and takes in the direction in which the force acts.
Force ∝ Change in momentum/ time taken
Consider a body of mass m having an initial velocity u. The initial momentum of this body will be mu. Suppose a force F acts on this body for time t and causes the final velocity to become v. The final momentum of this body will be mv. Now, the change in momentum of this body is mv – mu and the time taken for this change is t. So, according to Newton’s second law of motion:
F ∝ mv – mu/ t
F ∝ m(v – u)/ t
But v – u/ t represents change in velocity with time which is known as acceleration ‘a’. So, by writing ‘a’ in place of v – u/ t in the above relation, we get:
F ∝ m × a
F = k × m × a
F = m × a ( k= constant)
Force = mass × acceleration
Thus, Newton’s second law of motion gives us a relationship between ‘force’ and ‘acceleration’.
Newton’s second law of motion also gives us a method of measuring the force in terms of mass and acceleration.
F = m × a
a = F/m
The acceleration produced in a body is directly proportional to the force acting on it and inversely proportional to the mass of the body,
The SI unit of force is newton (N). A newton is that force which when acting on a body of mass 1kg produces an acceleration of 1 m/s2 in it.
F = m × a
1 newton = 1kg × 1m/s2
Newton’s second law gives us a relationship between the force applied to a body and the acceleration produced in the body.
If a minus sign comes with the force, it will indicate that the force is acting in a direction opposite to that in which the body is moving.
Application of newton’s second law of motion:-
- Catching a cricket ball
- The case of a high jumper
- The use of seat belts in cars
Example:- What force would be needed to produce an acceleration of 4m/s2 in a ball of mass 6 kg?
Sol:- Here, Mass = 6 kg
Acceleration = 4m/s2
Force = mass × acceleration
F = m × a
F = 6 × 4
F = 24 N
Thus, the force needed is of 24 newtons.
