elastic collision and kinetic energy

This should be simple but i just cant do it! Prove that an elastic head on collision between a neutron and a carbon atom which is initially stationary would result in the neutron losing about 72% of its kinetic energy to the carbon atom. I know that both KE and momentum are conserved but i can't seem to eliminate the unknowns in the equations! :s-smilie:

If any of you physicists out there can explain how it can be proved i'd be sooo grateful

Reply 1

Augmented hippo

2

Original post by lilangela

This should be simple but i just cant do it! Prove that an elastic head on collision between a neutron and a carbon atom which is initially stationary would result in the neutron losing about 72% of its kinetic energy to the carbon atom. I know that both KE and momentum are conserved but i can't seem to eliminate the unknowns in the equations! :s-smilie:

If any of you physicists out there can explain how it can be proved i'd be sooo grateful

I started by saying the neutron has mass m and velocity v. Carbon atom has mass 12m and is stationary. After collision I said neutron has velocity x and carbon atom has velocity y in the same direction of travel as the neutron was originally travelling in.
Using conservation of momentum

mv=mx+12my

This simplifies to

v=x+12y

Conservation of energy

\frac{mv^2}{2}=\frac{mx^2}{2}+6my^2

Simplifies to

v^2=x^2+12y^2

It sounds like you got this far but didn't know what to do next. The key is you want to know x in terms of v. You don't need to eliminate all the variables, just y.

Rearranging conservation of momentum for y gives