In the inertial frame of a space station a probe moves along the axis at the constant…

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

Relativity and Gravitation, Ch Minkowski spacetime, four-vectors and causal structure

Problem

In the inertial frame

S

of a space station a probe moves along the

+x

axis at the constant speed

0.400c

. Event

A

is the probe passing the station, at

t = 0

x = 0

. Event

B

is the probe passing a marker buoy that is at rest in

S

x = 8.00\ \mathrm{km}

. Draw a spacetime diagram of

S

with

x

horizontal and

ct

vertical, both in kilometres and to the same scale. Take

c = 2.998 \times 10^{8}\ \mathrm{m\,s^{-1}}

. ((a)) What is the slope

\mathrm{d}(ct)/\mathrm{d}x

of the probe's worldline on this diagram? ((b)) Read off the coordinates of

B

and hence compute the interval

\Delta s^2

between

A

and

B

\mathrm{km^2}

. ((c)) Find the time between the two events read by the probe's own clock.

Browse the problem library