Solve Elastic Collision Problem: Proton and Alpha Particle Kinetics

[richman614]

Please Help With PHYSICS PROBLEM!

I need help with a elastic collison problem I've tried and tried but can't seem to find a solution, so i figure i ask the smart kids.. Heres the question

2. Collisions between atomic particles are often perfectly elastic. In one such collision, a proton traveling to the right at 258 km/s collides head on with an alpha particle (a helium nucleus with mass 6.65x10^(-27)) intially at rest. Find the velocity of each particle after the collision. How much kinetic energy does the proton loose during the collision? Where does this energy go?

 

[mgb_phys]

Elastic means no energy is lost - so any energy lost by the first particle must go into the second particle.
The law of conservation of momentum says that the total momentum (mass * velocity) must be the same before and after the collision - although of course it may be shared differently between the two particles.

 

[kplooksafterme]

There are a pair of equations derived from both the conservation of momentum and energy expressions that you'll need to use here (they should be somewhere in your notes or textbook). What they'll tell you is that since the two masses are essentially equal, or close enough to being equal, that the velocity of the initially moving particle will be completely transmitted to the initially at rest particle. You should dig those equations out, or even better, derive them yourself (set the final velocity of the particle initially moving (particle 1)to v_1f = v_1i - m2/m1(v_2f), then plug this into the energy conservation expression.

Hope this helps.