Question

State Newton's second law of motion, in terms of momentum.

Answer 1

HINT- The second law states that the rate of change of momentum of a body is directly proportional to
the force applied OR Force equals mass times acceleration.

COMPLETE STEP BY STEP SOLUTION
According to the second law of motion the force applied on a body is proportional to the rate of change of momentum of the body.

ie; force $\propto$ change in momentum with respect to time
Or $F \propto \dfrac{{dp}}{{dt}}$ ……………………...(1)
Where p= momentum and we know that momentum is equal to the product of mass and velocity ie,P=mv
Putting the value of momentum in equation (1)
$F \propto \dfrac{{d(mv)}}{{dt}}$
Or $F = \kappa \dfrac{{d(mv)}}{{dt}}$ ………………….(2)
Where k is constant of proportionality
Since k=1 and mass is considered to be constant here so then in equation (2)

F = 1m \dfrac{{dv}}{{dt}} \\\ \Rightarrow F = m \dfrac{{dv}}{{dt}} \\\ \ $$ Since acceleration a measurement of how quickly an object is changing speed or change in velocity with respect to time ie; $$a = \dfrac{{dv}}{{dt}}$$ Therefore F=ma and Here, Force is directly proportional to mass and acceleration. Imagine a ball of a certain mass moving at a certain acceleration. This ball has a certain force If you double the mass, you double the force. If you double the acceleration, you double the force. And if you double the mass and the acceleration then, (2m)(2a) = 4F Doubling the mass and the acceleration quadruples the force. **Note :-** F = ma basically means that the force of an object comes from its mass and its acceleration Something very massive (high mass) that’s changing speed very slowly (low acceleration), like a glacier, can still have great force Something very small (low mass) that’s changing speed very quickly (high acceleration), like a bullet, can still have a great force. Something very small changing speed very slowly will have a very weak force