An electron ( ) is accelerated in a laboratory so that its speed rises from to

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

An electron (

m_ec^2 = 0.5110\ \mathrm{MeV}

) is accelerated in a laboratory so that its speed rises from

u_1 = 0.400c

u_2 = 0.800c

, both measured in the laboratory frame. A student says: "the speed has doubled, so the momentum doubles and the kinetic energy goes up by a factor of four." ((a)) Find

p_1c

and

p_2c

in MeV, and the ratio

p_2/p_1

. ((b)) Find

K_1

and

K_2

in MeV, and the ratio

K_2/K_1

. ((c)) Say in one sentence which step of the student's reasoning fails.

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