A rocket frame moves at along the common axis of the ground frame

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

Relativity and Gravitation, Ch Time dilation, length contraction and simultaneity

Problem

A rocket frame

S'

moves at

v = 0.500c

along the common

+x

axis of the ground frame

S

, the axes are parallel and the origins coincide at

t = t' = 0

(

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

). Two service lamps are fixed to the rocket at

x' = 0

(lamp

A

) and

x' = 480\ \mathrm{m}

(lamp

B

), with

B

ahead in the direction of motion. In the rocket frame both lamps flash at

t' = 0

, so the flash events in

S'

are

A: (t' = 0,\ x' = 0)

and

B: (t' = 0,\ x' = 480\ \mathrm{m})

. ((a)) Give the ground-frame coordinates

(t, x)

of the flash at lamp

B

. (The flash at

A

is at

(0, 0)

by the choice of origins.) ((b)) Give the distance between the two lamps as measured in the ground frame. ((c)) A student reads off your answer to (a) and says "the lamps are

x_B - x_A

apart in the ground frame". Using your two answers, say in one or two sentences why that figure is not the ground-frame length.

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