Two observers set out to observe cosmic phenomena. A muon traveling with a speed of 0.97c was observed to have a lifetime of 2.2 s (µ) and a maximum travel distance of 600 m in the muon's reference frame. Find:
a. The decay time, and
b. The decay distance measured by the Earth-based observer.
2. A spaceship is measured to be 100 m long while it is at rest with respect to an observer. Find the length of the spaceship when it flies by the observer with a speed of 0.95c.
3. An aluminum surface is illuminated with light of wavelength 200 nm. Find:
a. The kinetic energy of the ejected photoelectrons
b. The cut-off wavelength for aluminum
c. The maximum speed of the photoelectrons.
4. How fast must a meter stick be moving if its length is observed to shrink to 0.5 m?
5. A clock on a moving spacecraft runs 1 minute slower per day relative to an identical clock on Earth. What is the speed of the spacecraft? (Hint: For v/c = 1, note that γ^2 ≈ 1/(1 - v^2/c^2).)
6. An atomic clock is placed in a jet plane. The clock measures a time interval of 3600 s when the jet moves with a speed of 300 m/s. What corresponding time interval does an identical clock held by an observer on the ground measure?
7. A meter stick moving in a direction parallel to its length appears to be only 75 cm long to an observer. What is the speed of the meter stick relative to the observer?
8. A muon formed high in the Earth's atmosphere travels at speed v/c = 0.99 for a distance of 4.6 km before it decays into an electron, a neutrino, and an antineutrino (µ → e + ν + ν̄).
(a) How long does the muon live as measured in its reference frame?
(b) How far does the muon travel, as measured in its reference frame?
9. For what value of v does γ = 1.01?
10. An observer sees two particles moving in opposite directions, each with speed 0.9c. What is the speed of one particle with respect to the other?
Hints: Work functions (ϕ) of selected metals - Al: 4.08 eV, Cu: 4.70 eV, Fe: 4.50 eV