Particle Collisions: Proton Kinetic Energy + Carbon-12 Nucleus

[Liquidxlax]

Homework Statement

A proton with kinetic energy T₁ = 10MeV scatters elastically from a stationary carbon - 12 nucleus. The scattered proton emerges at 30^o to its initial direction.

a) Draw a sketch to represent the b4 and after conditions for this collision in the lab reference frame. Apply conservation of energy and momentum to find the kinetic energy of the scattered proton.

(Hint: to a good approximation you can assume the mass of carbon is 12x the mass of the proton. Use this as a mass scale to formulate your solution i.e. m₂ = 12m₁ etc. To further simplify, assume that the rest energy of the proton is m_pc² = 1000MeV. The kinematics in this problem are non relatavistic.)

b) What is the velocity of the centre of mass of this system?

c) same as a but find velocities in the centre of mass frame.

Homework Equations

conservation of nrg stuff...

The Attempt at a Solution

My only question is how does the rest energy come into play with this problem and how do i apply it. If it is non-relatavistic why do i even have rest energy? I have my momentum equations set up properly, just not my energy.

thanks

 

[Delphi51]

It seems clear that you do not need to use relativity or the rest mass.
I don't see a need for energy equations either - conservation of momentum in two dimensions should give you all the answers.

 

[Liquidxlax]

you sure i don't need rest energy? Oh and i need energy because c needs it. And are you sure i can solve it all with only 1 velocity 1 mass and an angle? I haven't done scattering in a while, and this is just review.

 

[Delphi51]

Sorry, I forgot about the second angle. You have two unknown speeds and one unknown angle, so you need 3 equations. Two momentum equations and, yes, the conservation of kinetic energy.

 

[Liquidxlax]

okay thanks Delphi51, I'm trusting you man