State the newton's second law of motion and give the mathematical equation also
Answers
Answer:
The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object
Explanation:
s = ut + 1/2 at2
Newton's second law of motion states that the rate of change of momentum of a body is directly proportional to the impressed force and takes place in the direction of force.
Now come to the point of the mathematical representation:
Let us assume that, the velocity of the body with mass 'm' change from 'u' to a distance from 'A' to 'B'.
So, we get that,
Initial velocity = u
Final velocity = v
Change in momentum = (Final momentum) - (Initial momentum)
= (mass × final velocity) - (mass × initial velocity)
= (m×v) -(m×u)
= mv - mu
∴ Rate of change of momentum = (mv-mu)/t
= m (v-u)/t
But,
(v-u)/t = (change in velocity/time) = a (acceleration)
∴ Rate of change of momentum = ma
According to the Newton's second law of motion,
F ∝ ma
or,
F = kma
Where, k = constant of proportionality.
By a suitable choice of units of F we can say that,
k = 1
∴ F = ma
∵ Force = Change in momentum/ time taken
∴ Change in momentum = force × time
It should have to be noted that,
Change in momentum is also can be said to be as impulse, which is equal to the product of force applied and the time for which it is applied.