# Determining beta as a function of relativistic momentum

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1. Sep 19, 2016

### Elvis 123456789

1. The problem statement, all variables and given/known data
For a fast moving particle, its momentum and energy are frequently easier to measure than its velocity.

a) Show that the factor of beta (as defined by β=v/c), can also be determined by measuring the ratio of relativistic momentum (p) and total energy (E).

b) Sketch, qualitatively, β as a function of p. (p is between 0 and infinity). You could choose a specific range of the momentum (in GeV/c), and assume the mass of the particle to be 1GeV/c2 . The shape and limit (for p=0 and infinity) of the function must be shown.

c) Think about, how would the mass of the particle change the curves?

2. Relevant equations
E = γ*m*c^2

P = γ*m*u

β = u/c
3. The attempt at a solution
P/E = β/c ------> β = c/E * P

this results in a linear relationship between β and P which I know isn't right. can anybody point me in the right direction?

2. Sep 20, 2016

### Orodruin

Staff Emeritus
Then you should reexamine this knowledge. You got the correct formula.

Note that the relationship is linear only because you are considering E and not m as the other variable and E and m have a non-linear relationship with P.