A bunch of ions travels at constant speed along a straight beam pipe

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

Relativity and Gravitation, Ch Minkowski spacetime, four-vectors and causal structure

Problem

A bunch of ions travels at constant speed along a straight beam pipe. The pipe is at rest in the laboratory frame

S

and has length

120.0\ \mathrm{m}

measured in

S

; in the bunch's rest frame the same pipe is

96.0\ \mathrm{m}

long. All motion is along the common

x

axis, both frames are inertial, and light travels in vacuum. ((a)) Find the bunch's speed as a multiple of

c

and its rapidity

\psi

relative to

S

. ((b)) In the laboratory frame, a detector clicks at

x = 0

t = 0

and a scintillator flashes at

x = 40.0\ \mathrm{m}

t = 0.2000\ \mu\mathrm{s}

. Compute

\Delta s^2

, classify the separation, and if a single clock can be present at both events give the proper time it would read. ((c)) The bunch emits light of wavelength

656.3\ \mathrm{nm}

measured in its own rest frame, and it is moving directly away from a laboratory spectrometer along the line of sight. What wavelength does the spectrometer receive?

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