The RHIC at Brookhaven is colliding fully ionized gold nucleiaccelerated to an e

Question

The RHIC at Brookhaven is colliding fully ionized gold nucleiaccelerated to an energy of 200 GeV per nucleon. Each Au nucleuscontains 197 nucleons.
(a) What is the speed of each Au nucleus just beforecollision? (b) What is the momentum of each at that instant? (c) What energy and momentum would be measured for one of theAu nuclei by an observer in the rest system of the other Aunucleus?
(a) What is the speed of each Au nucleus just beforecollision? (b) What is the momentum of each at that instant? (c) What energy and momentum would be measured for one of theAu nuclei by an observer in the rest system of the other Aunucleus?

Explanation / Answer

We have energy E = mc2 then = E/mc2    1/sqrt[1-v2/c2] =(197)(200GeV)(1.6*10-10J/GeV)/[(197)(1.67*10-27kg)(3*108m/s)2]       =212.9 or sqrt[1-v2/c2] =0.004697 or [1-v2/c2] =2.2*10-5      or v2/c2 = 0.9999779 or v = 0.9999889c

b) Momentum p = mv       =(212.9)(197)(1.67*10-27kg)(0.9999889)(3*108m/s)       = 2.1*10-14kgm/s or momentum p = sqrt[(E/c)2 +m2c2] plug in values
c) in ths case the reletaive speed of the other Au nucleus foran observer in one Au nucleus is vrel =(v+v)/(1+v.v/c2)                            = 0.9999999999c then =1/sqrt[1-(0.9999999999c)2/c2]    = 90089.59
Then plug in the values in the formula fof energy andmomemtum

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