Practice Special Relativity in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Special relativity is Einstein's theory describing physics at very high speeds, where measurements of time, length, and simultaneity depend on the observer's frame of reference.

At everyday speeds, classical physics works well. At speeds close to light, time and space behave differently from common intuition.

Showing a random 20 of 50 problems.

Example 1

medium
A muon's proper lifetime is 2×10−6 s2\times10^{-6} \text{ s}. At γ=5\gamma = 5, find its lifetime in the lab frame.

Example 2

medium
Find the energy equivalent of 0.5 kg0.5 \text{ kg} converted entirely to energy (c=3×108c = 3\times10^8).

Example 3

medium
A particle has rest mass m=1.67×10−27 kgm = 1.67\times10^{-27}\text{ kg} (a proton). Find its total energy at γ=4\gamma = 4. Use c=3.00×108 m/sc = 3.00\times10^8\text{ m/s}.

Example 4

medium
At what speed (as a fraction of cc) does γ=2\gamma = 2?

Example 5

medium
A rocket of proper length 100 m100\text{ m} passes Earth at v=0.6cv = 0.6c. What length does an Earth observer measure?

Example 6

easy
True or false: relativistic effects should be applied to a jogger running at 5 m/s5\text{ m/s}.

Example 7

medium
Find the kinetic energy of an electron (m=9.11×10−31 kgm = 9.11\times10^{-31}\text{ kg}) at γ=3\gamma = 3. Use c=3.00×108 m/sc = 3.00\times10^8\text{ m/s}.

Example 8

easy
An electron has mass m=9.11×10−31 kgm = 9.11 \times 10^{-31}\text{ kg}. Find its rest energy in joules. Use c=3.00×108 m/sc = 3.00 \times 10^8\text{ m/s}.

Example 9

challenge
A particle has momentum p=3mcp = 3mc. Find its total energy in units of mc2mc^2.

Example 10

challenge
A muon (γ=10\gamma = 10, proper lifetime 2.2×10−6 s2.2\times10^{-6} \text{ s}) moves at nearly cc. Find the distance it travels in the lab frame (c=3×108c = 3\times10^8).

Example 11

medium
A rod has proper length 2 m2 \text{ m}. Moving at γ=2\gamma = 2, find its contracted length.

Example 12

medium
Two events occur at the same place but at different times in frame SS. Are they simultaneous in any other inertial frame moving relative to SS?

Example 13

medium
A muon's proper lifetime is 2.2×10−6 s2.2\times10^{-6}\text{ s}. At v=0.99cv = 0.99c (γ≈7.09\gamma \approx 7.09), find its lifetime in the lab frame.

Example 14

easy
Find the Lorentz factor for v=0.95cv = 0.95c.

Example 15

medium
A pion has proper lifetime 2.6×10−8 s2.6\times10^{-8}\text{ s}. In a lab it travels 39 m39\text{ m} before decaying. Roughly what was its γ\gamma? (Use v≈c=3.00×108 m/sv \approx c = 3.00\times10^8\text{ m/s}.)

Example 16

medium
Find γ\gamma for v=0.99cv = 0.99c.

Example 17

easy
Find the Lorentz factor γ\gamma for an object moving at v=0.6cv = 0.6c.

Example 18

hard
A clock on a satellite runs at γ=1+5×10−11\gamma = 1 + 5\times10^{-11} slower than ground clocks. Roughly how many extra nanoseconds does the satellite clock lose per day relative to ground (consider only this γ\gamma effect)?

Example 19

easy
What postulate states that the speed of light is the same in all inertial frames?

Example 20

easy
Find the Lorentz factor for v=0.5cv = 0.5c.
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