Next: Example 2.2 Up: Relativistic dynamics Previous: Relativistic dynamics
As a simple example, consider two particles with rest masses and , moving with speeds and , which collide and coalesce [ see Figure 2.2 ]. What is the mass M and speed U of the resulting particle.
Figure 2.2: The colliding particles in Example 2.1.
The initial four- momenta are
The final four- momentum is
Conservation of four- momentum gives
and squaring this relation gives
For and , which is the usual Newtonian result. From the x and t components of the four- momentum equation we have
Dividing we get
For and we obtain