why dont we apply superposition principle to normal force?

 Imagine an elastic ball of mass m  falling freely from a height, the moment it strikes the ground, a normal force is applied which opposes the direction of motion, that normal force first decelerates the body to 0 speed and then provides the body an upward velocity due to which it bounces off the ground  

now suppose that the ball we are talking about approaches the ground at speed v remains in contact for a time t and bounces off at speed v, then we write the equation as

N(normal force) = m ( v- (-v))/t 

N = m(2v)/t .......(i)

But the main question is that during all the process in which the body strikes and bounces off, a downward force of gravity is acting on the ball which does not come in the dynamic equation shown above.

to answer this problem we look deeply into the time interval t in which the ball is in contact with the ground. One thing that is assumed is that the ball is elastic and so the time interval t is very very small and so if we carefully consider equation one then we can conclude that the term at the RHS is very very large and so even if we consider gravity and write it as

N- mg = m(2v)/t .....(ii)

then we can note that the normal force has to be very very large in comparison to gravity and so we neglect the force of gravity as it is very small in comparison to normal force and so we use equation 1 instead of equation 2.

THANKS FOR READING

-Arvin Gupta