| Date | May 2012 | Marks available | 2 | Reference code | 12M.3.HL.TZ2.16 |
| Level | Higher level | Paper | Paper 3 | Time zone | Time zone 2 |
| Command term | Show that | Question number | 16 | Adapted from | N/A |
Question
This question is about relativistic mechanics.
Show that the speed v of a particle of total energy E and momentum p is given by the following equation.
\[v = \frac{{p{c^2}}}{E}\]
[2]
a.
Determine, using the answer in (a), the speed of a particle whose rest mass is zero.
[2]
b.
Markscheme
combined use of p = γmv and E=γmc2;
eliminate the mass and gamma factor by, for example, dividing to get \(\frac{p}{E} = \frac{v}{{{c^2}}}\);
to get the result
Accept going backwards from given result to reach correct formulae.
a.
for a particle with zero rest mass, E=pc;
and so \(v = \left( {\frac{{p{c^2}}}{{pc}} = } \right)c\);
Award [1] for “zero rest mass particles are photons and so v = c”.
b.
Examiners report
a.
b.
Syllabus sections
Option A: Relativity » Option A: Relativity (Additional higher level option topics) » A.4 – Relativistic mechanics (HL only)
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