Calculate Velocity of Protons in CM Frame After Elastic Collision

In summary, in an elastic collision between two protons, the kinetic energy of each proton in the center of mass frame is equal to its rest energy. This means that the speeds of the protons will be equal and opposite. Using the relativistic energy momentum relationship, we can calculate the speed of the protons by equating their kinetic energy and rest energy. However, if we set the kinetic energy equal to the rest energy, we get a momentum of 0, which is incorrect. The correct equation should be c^2p^2 = m^2c^4.
  • #1
latentcorpse
1,444
0
proton mass 938MeV/c^2. Consider an elastic collision between two protons. IN the centre of mass frame the kinetic energy of each proton is equal to its rest energy.

calculate the speed of the protons in the CM frame.

clearly they will be equal and opposite velocities so the two speeds should be the same.

E=mc^2
then equate that to relativistic energy momentum relationship [itex]E=\sqrt{c^2p^2+m^2c^4}[/itex] but then i get p=0 so I am going wrong somewhere...
 
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  • #2
I assume you set E = the rest energy leading to p = 0. But it says the kinetic energy is equal to the rest energy, there's also it's rest energy!

(Kinetic energy + Rest energy) = sqrt(p^2 + m^2)
 
  • #3
do you mean i should have [itex]c^2p^2=m^2c^4[/itex]
 

FAQ: Calculate Velocity of Protons in CM Frame After Elastic Collision

What is the definition of velocity?

Velocity is a measure of the rate at which an object moves in a particular direction. It is a vector quantity, meaning it has both magnitude (speed) and direction.

What is the CM frame in the context of elastic collisions?

The CM (center of mass) frame is a reference frame in which the total momentum of a system is zero. In the context of elastic collisions, it is a frame of reference that is used to simplify the mathematical calculations by eliminating the need to consider the individual velocities of the colliding particles.

How is the velocity of protons in the CM frame calculated?

The velocity of protons in the CM frame after an elastic collision can be calculated using the conservation of momentum and energy equations. The initial and final momenta and energies of the protons are considered in the calculations to determine the velocities in the CM frame.

What is an elastic collision?

An elastic collision is a type of collision in which the total kinetic energy of the system is conserved. This means that the total energy before the collision is equal to the total energy after the collision. In an elastic collision, the colliding objects do not experience any permanent deformation or loss of energy.

Can the velocity of protons in the CM frame change during an elastic collision?

No, the velocity of protons in the CM frame remains constant during an elastic collision. This is because the CM frame is chosen to eliminate the effects of the individual velocities of the particles, so the total momentum and energy of the system are conserved without any changes in the velocity in the CM frame.

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