Einstein developed his theory of special relativity from two postulates. One postulate states that physical laws have the same form in all inertial frames.
State the other postulate and explain how it is consistent with the equation:
c=1μ0ε0 c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} c=μ0ε01A muon leaves a particle accelerator at point X and moves at a constant speed towards a target at point Y. The speed of the muon is 2.4×108 m s−12.4 \times 10^8 \text{ m s}^{-1}2.4×108 m s−1 in the frame of reference of the target. The distance XY in the frame of reference of the muon is 45 m45 \text{ m}45 m. The rest mass of a muon is 1.88×10−28 kg1.88 \times 10^{-28} \text{ kg}1.88×10−28 kg.
Calculate the distance XY in the frame of reference of the target.
Show that the kinetic energy EkE_{\mathrm{k}}Ek of the muon is about 1.1×10−11 J1.1 \times 10^{-11} \text{ J}1.1×10−11 J.
Sketch the variation of EkE_{\mathrm{k}}Ek with speed vvv for a muon. Your sketch should show both the classical prediction Ek=12m0v2E_{\mathrm{k}} = \frac{1}{2}m_0v^2Ek=21m0v2 (as a dashed line) and the relativistic curve (as a solid line) for speeds up to the speed of light c=3.0×108 m s−1c = 3.0 \times 10^8 \text{ m s}^{-1}c=3.0×108 m s−1. Identify the key differences between the curves.
22 exam-style questions on AQA A Level Physics Special relativity (A-level only), covering The Michelson-Morley experiment (A-level only), Einstein's theory of special relativity (A-level only), Time dilation (A-level only), Length contraction (A-level only), and Mass and energy (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.