
472 Classical Mechanics
T
MM MM c
M
th
1
34
2
12
2
=
+−+[( )( )]
where T
1
is the kinetic energy of the incident particle M
1
.
PROBLEMS
1. Two inertial frames S and S′ have their respective x-axes parallel with S′ moving with
constant velocity v along the positive x-direction of the system S. A rod makes an angle of
30° with respect to the x′-axis. What is the value of v if the rod makes an angle of 45° with
respect to the x-axis?
2. The wave equation
∇− =
2
2
2
1
0ψ
is satised in a vacuum for any component of
or
, and it is a consequence of Maxwell’s
equations. Show that this wave equation is invariant under a Lorentz transformation. For
simplicity ...