In the laboratory frame a beam of unstable hyperfragments travels in a straight line…

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

In the laboratory frame

S

a beam of unstable hyperfragments travels in a straight line along the

+x

axis at the constant speed

v = 0.800c

. Their mean proper lifetime (read by a clock riding with them) is

\tau_0 = 30.0\ \mathrm{ns}

. Two marker lamps are fixed to the beam pipe, one at

x_1 = 0

and one at

x_2 = 24.0\ \mathrm{m}

, and they are flashed simultaneously at

t = 0

S

. The rest frame of the hyperfragments is

S'

, in standard configuration with

S

S'

moves at

v = 0.800c

along the common

+x

axis and the origins coincide at

t = t' = 0

, so the flash of the first lamp is the event

(t, x) = (0, 0)

S

and the origin event of

S'

. The frames are inertial and gravity is ignored. Take

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

. ((a)) Find the mean lifetime of the hyperfragments as measured in the laboratory frame

S

. ((b)) Using the Lorentz transformation of Chapter 1, find the coordinates

x'

and

t'

of the second lamp's flash in

S'

. ((c)) Express the magnitude of the time between the two flash events in

S'

as a multiple of the mean proper lifetime

\tau_0

Browse the problem library