Frame is the rest frame of a particle laboratory

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Special relativity: spacetime and kinematics · Special relativity: spacetime and kinematics

Relativity and Gravitation, Ch The postulates and the Lorentz transformation

Problem

Frame

S

is the rest frame of a particle laboratory, and is inertial. A particle moves at constant velocity along the

+x

axis of

S

. It passes the origin at

t = 0

(event 1) and is recorded by a detector at

x = 1.20\times10^{3}\ \mathrm{m}

t = 6.00\ \mu\mathrm{s}

(event 2), both as measured in

S

. Take

c = 2.998\times10^{8}\ \mathrm{m\,s^{-1}}

. ((a)) An inertial frame

S'

in standard configuration with

S

moves at the speed

v

for which both events happen at

x' = 0

. Find

v

as a multiple of

c

and the time

t'

of event 2 in

S'

. What is

S'

, physically? ((b)) A second particle moves along the

x

axis at

0.900c

as measured in

S

. Find its velocity in

S'

, as a multiple of

c

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