Charged kaons have a mean proper lifetime (the mean lifetime read by a clock carried…

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

Charged kaons have a mean proper lifetime

\tau_0 = 12.4\ \mathrm{ns}

(the mean lifetime read by a clock carried with the kaon). In the laboratory frame

S

a kaon moves along the

+x

axis at the constant speed

v = 0.900c

, with

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

. The kaon's rest frame

S'

is in standard configuration with

S

. Both frames are inertial. ((a)) What is the mean lifetime of these kaons as measured in the laboratory frame

S

? ((b)) Two clocks are bolted to the beam line,

6.00\ \mathrm{m}

apart along

x

as measured in

S

, and they are synchronised with each other in

S

. At one instant of the kaon frame

S'

, by how much do their readings differ?

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