Tipler Chapter R & 39
Name: ________________________
#1 Unstable Particle
An unstable high-energy particle enters a detector and leaves a track of length 1.05 mm before
decaying. Its speed relative to the detector was found to be 0.992c.
a) Calculate the Lorentz factor of the particle.
b) Calculate the “proper lifetime” of the particle. (In other words, calculate the lifetime of the particle
had it been at rest relative to the detector.)
#2 Fast Electron
An electron having a speed parameter  = 0.999987 moves in a straight line through an evacuated tube
of length 3.00 m as measured by an observer in the laboratory at rest relative to the tube. An observer
at rest relative to the electron would see the tube moving by with the same speed parameter, (but in
the opposite direction). Calculate the length of the tube as seen by the observer moving with the
electron.
#3 Space Traveler
A space traveler leaves Earth in a ship and travels at v = 0.99c to the star, Vega which is 26 LY away from
Earth. How much time wil have elapsed on Earth when…
a) when the traveler reaches Vega;
b) when Earth observers receive the signal that the traveler has arrived at Vega.
c) How much older will the Earth observer calculate the traveler to be (as measured in the traveler’s
frame) when the traveler reaches Vega?
#4 Flashing Bulbs I
An experiment is set up to trigger two flash bulbs (one bright, the other not as bright) simultaneously.
The bright flash occurs at the origin and the dimmer flash occurs at x = 30.0 km as seen by a stationary
observer at rest in that frame. Another observer moving by at a speed of 0.250c in the +x-direction also
sees the flashes.
a) Calculate the time interval between the flashes according to the moving observer.
b) Which flash does the moving observer say happens first: the bright flash or the dimmer flash?
#5 Flashing Bulbs II
An observer in a stationary frame of reference detects two flashes of light. A bright flash occurs at x1 =
1200 m and, 5.00 s later, a dimmer flash occurs at x2 = 480 m. These two flashes of light are also
observed by an observer moving in the x-direction relative to the stationary frame. As detected by the
moving observer, the flashes occur at the same space location x’.
a) Determine the speed parameter  of the moving frame.
b) Determine whether the moving observer is travelling in the +x-direction or the –x-direction.
c) To the moving observer, calculate the time interval between the flashes.
d) To the moving observer, which flash occurs first?
#6 Receding Galaxies
Galaxy A is observer to be moving away from us at a speed of 0.35c. Galaxy B, which is located in exactly
the opposite direction, is found to be receding at exactly the same speed.
a) What is the speed parameter would an observer in Galaxy A report for our galaxy?
b) What speed parameter would an observer in Galaxy A report for Galaxy B?
#7 Energy of Electron
a) What is the speed of an electron that has been accelerated to the point at which its total energy is 4
times its rest mass? (The mass of an electron is 0.511MeV/c2.)
b) What is the electron's total energy at this velocity?
c) What is the electron's relativistic kinetic energy at this velocity?
d) Let's assume for a minute that Newtonian mechanics holds at this velocity. What would the
electron's Newtonian kinetic energy be at this velocity?
#8 Work
a) How much work must be done to increase the speed of an electron from 0.18c to 0.19c?
b) How much work must be done to increase the speed of an electron from 0.98c to 0.99c?
#9 Doppler Effect for Light
In the laboratory, a particle wavelength of light emitted from an oxygen atom is  = 513 nm. The
emission spectrum for oxygen coming from galaxy NGC 7319 has that same emission line shifted to 535
nm due to the Doppler effect. Calculate the radial speed of NGC 7319 relative to Earth and determine
whether NGC 7319 is approaching us or receding from us.