Relativistic Momentum and Energy

[Peter G.]

Hello guys,

The question is: What is the momentum, in conventional SI units, of a proton of momentum 685 MeVc^-1?

So, I tried two methods which yielded slightly different answers, both proximate to the actual answer (3.66 x 10^-19)What I first tried to do was to rearrange: ρ=γm₀v

To find the particles velocity and then multiply it by the proton's rest mass in kg. I got 2.995 x 10^-19 kgms^-1

The second method, which gave me the result 3.45 x 10^-19 kgms^-1 was the following:

From: E² = (m₀)²c⁴ + p²c² I got a value for total energy. I then subtracted the rest energy from that and I got a value for KE.

I equalled that to p²/2m and solved for p (using m in kg and the energy converted from MeV to J)

Are my answers wrong? The book says 3.66 x 10^-19 and I simply can't get that!

Thanks in advance!

 

[NoPoke]

the book answer is correct.

a question for you : What does MeVc-1 mean?

can you do a dimension analysis on MeVc-1

 

[Peter G.]

Oh, got it! Thanks! I got the number!

 

[Peter G.]

Oh, and, if you don't mind, could you (or anyone else) help me with the following problem please?

A proton initially at rest finds itself in a region of uniform electric field of magnitude 5.0 x 10⁶ Vm^-1. The electric field accelerates the proton for a distance of 1 km.

Find the kinetic energy of the proton.

So, what I did was the following:

KE = q * E * s

I then converted the result from J to MeV. I, however, get 5000 MeV and the book gets 500 MeV. Is my line of thought incorrect?

Thanks once again!