Determining beta as a function of relativistic momentum

[Elvis 123456789]

Homework Statement

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?

Homework Equations

E = γ*m*c^2

P = γ*m*u

β = u/c

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?

 

[Orodruin]

which I know isn't right

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.