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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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