A charged pion has a mean proper lifetime

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

\tau_0 = 26.0\ \mathrm{ns}

, that is, the mean lifetime read by a clock riding with the pion. In the laboratory frame

S

a pion travels in a straight line along the

+x

axis at the constant speed

v = 0.980c

, with

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

. Let

S'

be the pion's rest frame, in standard configuration with

S

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

S

? ((b)) Two detectors sit on the beam line,

45.0\ \mathrm{m}

apart along

x

as measured in

S

. Their lamps flash simultaneously in

S

. What is the magnitude of the time interval between the two flashes as measured in the pion frame

S'

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