Newton’s Second Law of Motion
This law describes the relationship between an object’s mass and the amount of force needed to accelerate it. Newton’s second law is often stated as the rate of change of momentum of a body is directly proportional to the applied force, and takes place in the direction in which the force acts.
Mathematically, F= ma
Which means ‘F’ acting on an object is equal to the mass (m) of an object times its acceleration (a). Therefore, the more mass an object has the more ‘F’ you need to accelerate it. And the greater the F is, the greater is the object’s acceleration.
Suppose,
Mass of an object = m kg
Initial velocity of an object = u m/s
Final velocity of an object = v m/s
Initial momentum, p_{1 }= mu,
Final momentum, p_{2 }= mv
So, Change in momentum = Final momentum – Initial momentum
= mv – mu
= m(v – u)
∴ Rate of change of momentum = Change in momentum/ Time taken
= m(v – u)/ t
According to 2^{nd} law of motion, this rate of change is momentum is directly proportional to force.
∴ F ∝ [m(v – u)/ t]
We know that, (v – u)/ t = a (From 1^{st} equation of motion)
So, F = kma
Where k is a constant. Its value = 1.
∴ F = 1 × m × a = ma
F = ma
1 Newton: When an acceleration of 1 m/s^{2 }is seen in a body of mass 1 kg, then the force applied on the body is said to be 1 Newton.
Proof of Newton’s First Law of Motion from Second Law
First law states that if external force F = 0, then a moving body keeps moving
with the same velocity, or a body at rest continues to be at rest.
We know, F = [m(v – u)/ t]
As, F = 0
So, 0 = [m(v – u)/ t]
or, v = u
Thus, final velocity is equal to initial velocity.
If body is initially at rest i.e., u = 0. Then, u = v = 0. So, the body will continue to be at rest.
Newton’s Second Law of Motion in Everyday Life:
(a) A fielder pulls his hand backward; while catching a cricket ball coming with a great speed, to reduce the momentum of the ball with a little delay. According to Newton’s Second Law of Motion; rate of change of momentum is directly proportional to the force applied in the direction.
While catching a cricket ball the momentum of ball is reduced to zero when it is stopped after coming in the hands of fielder. If the ball is stopped suddenly, its momentum will be reduced to zero instantly. The rate of change in momentum is very quick and as a result, the player’s hand may get injured. Therefore, by pulling the hand backward a fielder gives more time to the change of momentum to become zero. This prevents the hands of fielder from getting hurt.
(b) For athletes of long and high jump sand bed or cushioned bed is provided to allow a delayed change of momentum to zero because of jumping of athlete.
When an athlete falls on the ground after performing a high or long jump, the momentum because of the velocity and mass of the athlete is reduced to zero. If the momentum of an athlete will be reduced to zero instantly, the force because of momentum may hurt the player. By providing a cushioned bed, the reduction of the momentum of the athlete to zero is delayed. This prevents the athlete from getting hurt.
(c) Seat belts in the vehicles prevent the passenger from getting thrown in the direction of motion. In case of emergency, such as accidents or sudden braking, passengers may be thrown in the direction of motion of vehicle and may get fatal injuries. The stretchable seat belts increase the time of the rate of momentum to be reduced to zero. The delayed reduction of momentum to zero prevents passengers from such fatal injury.