| course |
course_year |
question_number |
tags |
title |
year |
Special Relativity |
IB |
41 |
IB |
2001 |
Special Relativity |
|
4.II.18F |
2001 |
A particle of mass $M$ is at rest at $x=0$, in coordinates $(t, x)$. At time $t=0$ it decays into two particles $\mathrm{A}$ and $\mathrm{B}$ of equal mass $m<M / 2$. Assume that particle A moves in the negative $x$ direction.
(a) Using relativistic energy and momentum conservation compute the energy, momentum and velocity of both particles $A$ and $B$
(b) After a proper time $\tau$, measured in its own rest frame, particle A decays. Show that the spacetime coordinates of this event are
$$\begin{aligned}
t &=\frac{M}{2 m} \tau \\
x &=-\frac{M V}{2 m} \tau,
\end{aligned}$$
where $V=c \sqrt{1-4(m / M)^{2}}$.