Relativistic energy and momentum conservation

[denniszhao]

Summary:: this is what I've done so far... i don't think it works since i believe the information given is not even enough.
the formula I've used are
1. relativistic total energy = rest mass energy + kinetic energy (line 1, 3)
2. conservation of energy (line 4, 7, 8, 9)
3. conservation of momentum (line 5, 6)

 

[Ibix]

I take it the second particle is a proton, not a photon. You don't seem to have written down the total initial momentum. What is it?

You also seem to be trying to apply ##\gamma mc^2## to the photon, which is not correct since ##\gamma## is undefined for photons.

 

[denniszhao]

ohh you're right.. the second particle is actually a proton

 

[pervect]

This looks like it should be in the homework forum.

Comments: Look up and write down for us the correct formula for the total energy E and total momentum P of a particle of a massive particle of rest mass m_0 with a velocity v and an associated gamma factor of ##\gamma = 1/\sqrt{1-v^2 / c^2}##.

You'll also need the relationship between the energy and momentum of a photon.

There's no need to split the energy into a kinetic and rest part as you did in line 1. The usual formula that you should look up in your textbook (I am assuming you have a textbook) gives the total energy. Your text should also give you the relationship between momentum and energy of a photon.

Find the total energy and total momentum of the system of photon and proton by adding the energy of the photon to the total energy of the proton. Find the total momentum of the inital system in a similar manner.

I would assume that the intent of the problem is that there are no other particles created, so if you equate the energy and momentum of a single massive particle to the sum of the energies and the sum of the momenta in your initial system, you'll have the problem set up correctly.

 

[PeterDonis]

This looks like it should be in the homework forum.

Agreed. Thread has been moved to the homework forum.

 

[PeroK]

Summary:: this is what I've done so far... i don't think it works since i believe the information given is not even enough.
the formula I've used are
1. relativistic total energy = rest mass energy + kinetic energy (line 1, 3)
2. conservation of energy (line 4, 7, 8, 9)
3. conservation of momentum (line 5, 6)

View attachment 265308

Try using the energy-momentum relations. Remember that for all particles we have:
$$E^2 = p^2c^2 + m^2c^4$$

 

[neilparker62]

Just by way of interest, is there a unit of momentum which one can use alongside (M)eV as the unit of energy ? Since p = E/c , it should be something like eV s / m. One of the complications of problems such as the above is switching between normal SI units and eV.

 

[PeroK]

Just by way of interest, is there a unit of momentum which one can use alongside (M)eV as the unit of energy ? Since p = E/c , it should be something like eV s / m. One of the complications of problems such as the above is switching between normal SI units and eV.

Yes, the unit of momentum is ##MeV/c##. And the unit of mass is ##MeV/c^2##.

 

[neilparker62]

$$\sin\delta=\frac{500}{1438}$$