Find Rest Mass of Composite Particle After Collision

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In summary, the conversation discusses finding the rest mass M of a composite particle after a collision between a stationary particle of rest mass 2m and a moving particle of rest mass m and kinetic energy 2mc^2. Using conservation of momentum and energy equations, the solution involves finding the initial velocity of the moving particle and then using the total energy of the system before the collision to solve for M and v2.
  • #1
Joules6626
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Homework Statement


A particle of rest mass m and kinetic energy 2mc^c strikes and sticks to a stationary particle of rest mass 2m. Find the rest mass M of the composite particle


Homework Equations


E = mc^2 + KE
E^2 = (mc^2)^2 + (pc)^2
p = mv/sqrt(1-v^2/c^2)


The Attempt at a Solution


For finding the initial velocity of the moving particle:
2mc^2 = KE = mc^2/sqrt(1-v^2/c^2) - mc^2
m's cancel
and when solving for v, you get v1 = sqrt(2/3)c

To find M, I tried using conservation of momentum and energy.
p1 = p2
mv1/sqrt(1-v1^2/c^2) + 2m*0 = Mv2/sqrt(1-v2^2/c^2)
I can't seem to find a way to make the equation only have one unknown.
 
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  • #2
Where's your conservation of energy equation?
 
  • #3
E1 = E2
(mc^2)^2 + (cmv1/sqrt(1-v1^2/c^2))^2 = (Mc^2)^2 + (cMv2/sqrt(1-v2^2/c^2))^2
 
  • #4
That's not quite right. You forgot the energy of the stationary mass. Also, to simplify the algebra, you might want to use E=γmc2 rather than breaking out the rest energy and momentum contributions separately.
 
  • #5
so it would be
(mc^2)^2 + (cmv1γ1) + 2mc^2 = (Mc^2)^2 + (cMv2γ2)^2?
how would that give me a function of just v2 or M?
 
  • #6
No, that's still not right. It doesn't work out unit-wise. You have quantities equal to E2, not E. Plus you're making it more complicated than it needs to be. You can calculate the total energy of the system before the collision just by adding up a few quantities you were given.

You have two equations and two unknowns (M and v2). Now it's just a bunch of algebra to solve for them.
 

1. What is a composite particle?

A composite particle is a type of particle that is made up of smaller subparticles, such as protons, neutrons, and electrons.

2. How is the rest mass of a composite particle calculated?

The rest mass of a composite particle is calculated by adding up the rest masses of all the subparticles that make up the composite particle.

3. What is the significance of finding the rest mass of a composite particle after a collision?

Finding the rest mass of a composite particle after a collision allows scientists to understand the energy and momentum conservation in the collision, which can provide insights into the fundamental laws of physics.

4. Can the rest mass of a composite particle change after a collision?

Yes, the rest mass of a composite particle can change after a collision due to the conversion of mass into energy, as described by Einstein's famous equation E=mc².

5. How do scientists measure the rest mass of a composite particle after a collision?

Scientists typically use particle accelerators and other advanced technologies to study collisions and measure the rest mass of composite particles. They analyze the data collected from these experiments using mathematical models and equations.

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