In frame two protons

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Special relativity: spacetime and kinematics · Relativistic dynamics and fields in flat spacetime

Relativity and Gravitation, Ch Relativistic momentum, energy and collisions

Problem

In frame

S

two protons, each of mass

938.3\ \mathrm{MeV}/c^2

, move along the

+x

axis: proton A at

0.600c

and proton B at

0.800c

. Frame

S'

is in standard configuration with

S

, moving at

v = 0.600c

along

+x

, so that proton A is at rest in

S'

. Treat both protons as free particles. ((a)) Find the total energy

E_{\rm tot}

and the total

p_{\rm tot}c

of the two-proton system in

S

, both in MeV. ((b)) Find the invariant mass of the system, in

\mathrm{MeV}/c^2

. ((c)) Using the velocity transformation of Chapter 1, find the speed of proton B in

S'

, as a multiple of

c

. ((d)) Transform the total four-momentum to

S'

with the Lorentz transformation for four-vectors (Chapter 3) and give

E'_{\rm tot}

and

p'_{\rm tot}c

in MeV. Confirm that the invariant mass of (b) is unchanged.

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