Mandelstam Variable Calculation in Proton Scattering

[EmmaK]

Homework Statement

In a scattering experiment the square-root of

(i)Consider a proton of (relativistic) energy,E, incident on another proton in a stationary target. Show that in this case, s= 2m_p(m_p+E/c^2) where m_p is the proton mass.
(ii)Now consider 2 protons traveling with equal and opposite momenta, each of energy E which collide head-on. Calculate the value of s.
(iii)Using the answers to parts (i) and (ii) consider experiments with highly relativistic proton beams, and comment on the relative advantage of two colliding beams over a single beam incident on a fixed target, in searches for new undiscovered types of elementary particles
(iv)In what important way does the comparison in part (iii)differ here compared to the case of classical Galilean kinematics?

Homework Equations

s=(p1+p2)^2
E=pc
E=mc^2 (stationary proton)
E^2=p^2c^2+m_p ^2c^4 (moving proton)

The Attempt at a Solution

I've tried rearranging the formulae to get value of p for each proton, then subbing it into the first equation, but i just can seem to get it to work

 

[Ant1508]

Lol, came across this looking for help with it!
I managed to get to the first answer by using the equation for s which we were given in lectures:
s=((Total Relativistic Energy)^2-(Total Momentum)^2)/c^2
Just sub in E and p and it should work, repeat for question 2.
I believe question 2 is sorted by assuming that in high energy, the mass of the particles is irrelevant, and the latter gives more energy.

 

[EmmaK]

Still not working lol! must be doing something really stupid

 

[vela]

What do you have for p1 and p2?

 

[EmmaK]

got it :)