Notes
• CIFs are still open – please fill them out
• Final Exam: Tuesday, May 8, 1:45pm, Here.
• Review Session: NSH 184, Monday, May 7,
7:30-9:30pm
At the LHC protons will be accelerated to energies of
7 TeV (= 1012 eV). The rest mass of a proton is 938
MeV/c2. What fraction of the speed of light will the
protons have?
A proton of mass m is accelerated in a proton
synchrotron to a total energy E and strikes a second
target proton that is at rest. Assume a single particle of
mass M is produced. Find the mass M in terms of the
initial mass and energy.
A proton of mass m is accelerated in a proton storage
ring to a total energy E and strikes a second proton that
is counter-rotating with the same energy. Assume a
single particle of mass M is produced. Find the mass M
in terms of the initial mass and energy.
An accelerator produces a beam of neutral kaons (mKc2
= 498 MeV/c2) with kinetic energy 325 MeV. Consider
a kaon that decays in flight into two pions (mc2 = 140
MeV/c2). Find the kinetic energy of each pion in the
special case where the pions travel parallel or antiparallel to the kaon beam.
A cube of steel has a volume of 1.00 cm3 and a mass of
8.0g when at rest. This cube is now given a speed of
0.900c. What is its density as measured by a stationary
observer?
A moving rod is observed to have a length of 2.00m and
to be oriented at an angle of 30° with respect to the
direction of motion. The rod has a speed of 0.995c
relative to this frame. (a) What is the proper length of
the rod? (b) What is the orientation angle in the rest
frame of the rod?
How much mass must be converted into other forms of
energy in order to keep a standard 100W light bulb
burning for a century?
A pion (mass 138 MeV/c2) at rest decays to a muon (mass 106
MeV/c2) and a muon anti-neutrino (mass  0). Find the kinetic
energies of the muon and neutrino.
An unstable particle with mass 1.876 GeV/c2 is initially at rest.
The particle decays into two fragments that fly off along the x
axis with velocity components u1 = 0.987c and u2 = - 0.868c.
From this information
information, we wish to determine the masses of
fragments 1 and 2. (a) Find the values of  for the two fragments
after the decay.
y ((b)) Using
g total momentum conservation,, find a
relationship between the masses m1 and m2 of the fragments. (c)
Using energy conservation, find a second relationship between
the masses m1 and m2. (d) Solve simultaneously for the masses
m1 and m2.
Imagine that the entire Sun collapses to a sphere of
radius Rg such that the work required to remove a small
mass m from the surface of the star is equal to its rest
mass. This is called the “gravitational radius” of the
star. Find Rg for the Sun. This gives a length scale for
the size of a black hole formed from a star of a given
mass.