Comparing Impacts: Momentum vs. Kinetic Energy

[lozzajp]

Homework Statement

What is more likely to cause greater injury, a collision with a light person at fast speed or a person with twice the mass at half the velocity?

Homework Equations

momentum = mv
KE = 1/2mv^2

The Attempt at a Solution

I am having a little trouble at which is appropriate here. I know momentum will be the same regardless, so if you are hit by either person you should travel backwards at the same velocity (your mass does not change)?

Where as the other hand the lighter person has more kinetic energy, so do they pack a harder initial punch so to speak?

I am more interested in understanding the difference between momentum and KE during a collision?

Thanks everyone.

 

[clamtrox]

What happens when the total kinetic energy is not conserved in a collision? Where does the energy go?

 

[lozzajp]

heat, sound and things.

but a higher kinetic energy results in more "damage", where as the person will still be knocked back at the same velocity as momentum is the same. I can't quite get my head around it :/

 

[clamtrox]

So let's consider for simplicity a completely inelastic collision. Then the two colliding particles stick together and continue moving as a single object after collision. Can you calculate how the change in kinetic energy looks like in terms of the masses of colliding bodies and the initial momentum?

 

[lozzajp]

person 1, 100kg 10m/s. person 2 50kg (made these up on spot)

KE = 50kg x 100m/s
KE = 5000kJ
(person 2 has 0)

post collision, 150kg, 6.7m/s

KE = 75kg x 44.89m/s
KE = 3366.75kJ

a person double the mass and half the velocity only has a KE of 2500kJ?

 

[clamtrox]

So in the initial collision, there is some amount of energy released. The person who was hit also gains some extra kinetic energy (if you want to also consider him falling over etc.) but that should be pretty easy to calculate too.

So now the change in kinetic energy is something like 1600 kJ. How about if person 1 weighs 10 kg and is moving at 100m/s?

OK, after that it should be pretty clear that there's more kinetic energy released in that impact. Here's a bonus problem for you: what about if the person weighs 1kg and moves at 100m/s compared to 100kg and 10m/s? Then the kinetic energies are equal. Which impact releases more energy?