A proton ( ) moves along the axis of the laboratory frame with speed

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

Relativity and Gravitation, Ch Relativistic momentum, energy and collisions

Problem

A proton (

m_pc^2 = 938.3\ \mathrm{MeV}

) moves along the

+x

axis of the laboratory frame with speed

u = 0.900c

. It is a free particle. ((a)) Construct its four-momentum in the laboratory frame: give

E

in MeV and

p_x

\mathrm{MeV}/c

(with

p_y = p_z = 0

). ((b)) Find its kinetic energy

K

in the laboratory frame. ((c)) A student writes: "at

0.900c

the proton's mass has grown to

M = \gamma m_p

, so its kinetic energy is

\tfrac{1}{2}Mu^2

." Evaluate the number the student's recipe gives, in MeV, and state what is wrong with the recipe.

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