Special Relativity
Kinematics Problems
1. A K meson has an initial kinetic energy of 2,000 MeV. It collides with a stationary proton,
and the two particles fuse to form a hyperon Σ. What is the mass of the Σ? What is its velocity?
K + p → Σ
2. A Λ hyperon has an initial momentum of 3,000 MeV. It decays into a proton and a π meson.
In the center of mass of the Λ, the two decay products emerge at right angles to the direction of
the incident hyperon. What is the angle of the proton and the π in the laboratory frame, with
respect to the incident Λdirection?
Λ → p + π
3. A π+ meson is traveling in the laboratory with a kinetic energy of 1,000 MeV, and decays into
a positron e+ and a neutrino ν. The neutrino emerges in the direction of the incident meson.
What is the neutrino energy?
π+ → e+ + ν
4. In a colliding beam experiment, an electron and a positron collide head-on in the lab. Each
incident particle has a momentum of 100 GeV = 105 MeV. What is the largest mass particle that
can be produced in the final state of such a collision?
5. A space ship traveling at a velocity v = 0.8 c is struck by a 1 gram meteor traveling in the
opposite direction with a velocity of 10-4 c (the escape velocity of our solar system, typical of
meteors). Calculate the kinetic energy of the meteor in the ship’s frame of reference. Try to find
the energy release of a stick of dynamite and compare the two. Is this a hazard for interstellar
missions?
6. Ion beam implantation is a process that is used extensively in the manufacture of silicon
microcircuits. Oxygen ions of kinetic energy 5 MeV are used in a particular process. How much
energy is lost by such an ion if it scatters head-on with an electron that is initially at rest
(typically attached weakly to a gas molecule)?
Masses in MeV/c2:
O 16,000
Λ 1115
p 938
K 511
π 130
e 0.5
ν 0
