# Homework Help: Momentum or kinetic energy?

1. Oct 23, 2012

### lozzajp

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
momentum = mv
KE = 1/2mv^2

3. 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.

2. Oct 23, 2012

### clamtrox

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

3. Oct 23, 2012

### 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 cant quite get my head around it :/

4. Oct 23, 2012

### 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?

5. Oct 23, 2012

### 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?

6. Oct 24, 2012

### 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?