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Old Feb 2nd 2011, 06:46 PM   #1
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Momentum and KE: relativistic vs classical

I have the following question in physics that i can't quite get the answer for and was hoping someone could explain the method.


and electron and proton are each accelerated through a potential difference of X volts. Find the momentum in MeV/c and kinetic energy of each. Compare these results to those of classical physics.

Any help would be awesome.
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Old Feb 3rd 2011, 12:55 PM   #2
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Originally Posted by abradshaw View Post
I have the following question in physics that i can't quite get the answer for and was hoping someone could explain the method.


and electron and proton are each accelerated through a potential difference of X volts. Find the momentum in MeV/c and kinetic energy of each. Compare these results to those of classical physics.

Any help would be awesome.
To do a Classical (or relativistic as well) treatment of this we are going to need to know how far the particle has traveled. Let's call this distance d. Then we have that the work done on a particle is
W = qX = (1/2)mv^2 - (1/2)mv0^2

Setting v0 = 0 m/s for simplicity we get
qX = (1/2)mv^2 = K <-- Kinetic energy

v = [2qX/m]^(1/2)

which implies
p = mv = [2mqX]^(1/2) <--Momentum

To do this Relativistically W = change in total energy E = qX. Again setting v0 = 0 m/s we get
W = qX = E - m0c^2

where m0 is the rest mass and E is the total energy after moving a distance d in the potential. Then
E = [p^2c^2 + (m0c^2)^2]^(1/2)

Solving this for p gives the momentum.

Now p = (gamma)m_0v so we get v. (Recall that gamma depends on v.) Finally K = ((gamma) - 1)E is your kinetic energy.

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Old Feb 4th 2011, 12:38 PM   #3
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Thanks for your help, that cleared everything up.
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