Physics HELP!
posted by Allison .
You are at the controls of a particle accelerator, sending a beam of 3.90×10^7 m/s protons (mass m ) at a gas target of an unknown element. Your detector tells you that some protons bounce straight back after a collision with one of the nuclei of the unknown element. All such protons rebound with a speed of 3.60×10^7 m/s . Assume that the initial speed of the target nucleus is negligible and the collision is elastic.
a)Find the mass of one nucleus of the unknown element. Express your answer in terms of the proton mass m.
b)What is the speed of the unknown nucleus immediately after such a collision?

Let the final velocity of the gas atom be V, and its mass be a*m, where a is a constant and m is the proton mass. Linear (x) momentum and total kinetic energy are conserved. Use classical mechanics since velocities are less than 0.15c, and because I am lazy.
m*3.9*10^7 = m*3.7*10^7 + a*m*V
(1/2)m*(3.9)^2*10*14 = (1/2)*m*(3.7)^2*10^14 + (a*m/2)V^2
Cancel out the m's.
7.6*10^7 = a V
15.21*10^14 = 13.69*10^14 + a V^2
1.52*10^14 = a V^2
57.76*10^14 = a^2 V^2
a = 38
V = 2.00*10^6 m/s
A relativistic solution might be slightly different.