Charged pions of proper mean lifetime (read by a clock riding with the pion) are…
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 pions of proper mean lifetime τ0=26.0ns (read by a clock riding with the pion) are produced at the origin of the laboratory frame S and travel at v=0.8c along the common +x axis. The pion rest frame S′ is in standard configuration with S: it moves at 0.8c along +x and the origins coincide at t=t′=0. Two markers are fixed on the beam line at x=0 and x=10.4m in S, each carrying a clock synchronised in S; consider the two events "the clock at x=0 reads t=0" and "the clock at x=10.4m reads t=0". Take c=2.998×108ms−1.
((a)) Find the mean lifetime of these pions in the laboratory frame.
((b)) Find the mean distance a pion travels in the laboratory before decaying.
((c)) Using the Lorentz transformation, find the times t′ of the two marker events in the pion frame, and state which marker clock's zero-reading happens first in that frame.