What is the mass of the unknown particle? ?

Question

A proton is traveling at a certain velocity and collides with an unknown particle. Given is both the velocity of the proton and the particle. Question is: what is the mass of the unknown particle?

What formula is used to solve this? Can you show an example by making up the velocities.

Answer 1

You have to use conservation of energy and conservation of momentum.  Assume only the proton is moving to start with.  I'll assume the particles are moving in a line (although you don't say, they could go off at angles).

Initial momentum = mproton v1proton

=

Final momentum = mproton v2proton + mparticle v2particle

Initial kinetic energy = 1/2 mproton v1proton^2

=

Final kinetic energy = 1/2 mproton v2proton^2 + 1/2 mparticle v2particle^2

So you have two equations.  It sounds like you only have one unknown, so you could use either equation to solve for the masas of the particle.  If there's something else you don't know, you can solve the system of 2 equations and 2 unknowns.

Answer 2

♦ momentum of proton-particle system is L=p*u1 +m*v1, where p is mass of proton, m is mass of particle, vector u1=|u1|*(1,0) is velocity of proton, and vector v1=|v1|*(cos(b1), sin(b1)) is velocity of particle before collision;

♠ momentum of proton-particle system after collision is L=p*u2 +m*v2, where vector u2=|u2|*(cos(a), sin(a)) is velocity of proton, and v2=|v2|*(cos(b2), sin(b2)) is velocity of particle;

♣ since momentum conserves L=L;

p*u1 +m*v1 = p*u2 +m*v2, hence 2 equations:

1) p*(|u1| -|u2|*cos(a)) = m*(|v2|*cos(b2) -|v1|*cos(b1)), hence

m= p*(|u1| -|u2|*cos(a)) /(|v2|*cos(b2) -|v1|*cos(b1));

2) p*(0 -|u2|*sin(a)) = m*(|v2|*sin(b2) -|v1|*sin(b1)), hence

m= -p*|u2|*sin(a) /(|v2|*sin(b2) -|v1|*sin(b1));

you must get the same m from either of these equations;