A ball falls on ur head, is it better for it to stick or bounce off in terms of inelastic & elastic collisions

Question

This is a phyics question having to due with conservation of momentum and kinetic energy. Can you justify your anwser y it is better one way or another!

Answer 1

Ok, we're going to need some information, first. We're going to assume that you are stationary to make the calculations simpler.


m = mass of ball
M = Mass of your head
v = velocity of ball on impact
t = duration of impact


In the elastic collision, conservation of momentum tells us

-mv = mv' - MV'

v' = speed of ball after collision
V' = speed of your head after collision

Solving for V'

V' = m(v + v')/M

The force experienced by your head is

F = Ma = M (V/t) = m(v + v')/t


We need to compare this with the force experienced during an inelastic collision.

mv = (m + M)V

V = speed of the head/ball system after the collision

V = mv(m + M)

The force felt by your head is

F = (m + M)a = (m + M)V / t = mv / t



To recap:

Felastic = m(v + v')/t
Finelastic = m v /t

The force felt during an inelastic collision (bouncing off) is greater, due to the speed the ball leaves your head.

Think of it this way... in an inelastic collision, the ball doesn't bounce off your head, so v' = 0. So it's hurts less if the ball bounces off rather than sticks.

Answer 2

If it sticks it means it is inelastic and if it bounces off it is elastic. Perfect elasticity means that all energy stays in the object. Perfect inelasticity means that all the energy transfers. Perect inelasticity is better, I think, because if it were me I could stop moving.

Answer 3

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