Calculate Momentum/KE Transfer in Neutron-Boron Collision

[richylai]

A neutron with a mass of 1.67×10^−27 kg and moving with a speed of 45000 m/s makes a head-on collision with a boron nucleus with a mass of 1.66×10^−26 kg. The boron nucleus is originally at rest.

If the collision is perfectly elastic, what fraction of the neutron's original kinetic energy is transferred to the boron nucleus?

 

[berkeman]

What equations apply? You need to show your work before we can offer tutorial help.

 

[richylai]

I used the conservation of momentum equation, M neutron * Vi,n = M neutron * Vf,n + M boron * Vf,b

Then I would use the KE equation .5(M neutron)(Vi,n)^2 = .5(M neutron)(Vf,n)^2 + .5(M boron)(Vf,b)^2

However, I realized that I would be messing with two unknowns and I have no idea how to approach that, unless I'm totally off with the equations I presented.

 

[Hootenanny]

You indeed have two unknowns, but you also have two equations, which you can solve simultaneously.

 

[richylai]

Ah... Ok, I guess I have to do some kind of substitution.

 

[Hootenanny]

Ah... Ok, I guess I have to do some kind of substitution.

That would be the way forward...

 

[richylai]

Oh no... Looks like I have to use the quadratic formula for this... -.-'