Question
Assuming that the Lorentz factor becomes significant if it affects measured lengths and times at the $10 \%$ level (a Lorentz factor value of 1.1 ), how fast must the observed speed of an object be to reach this threshold?
Step 1
The Lorentz factor is given by the equation: γ = 1 / √(1 - v²/c²) where γ is the Lorentz factor, v is the velocity of the object, and c is the speed of light. Show more…
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Figure 18.6 shows how the Lorentz factor depends on speed. At about what speed (in terms of $c$ ) does the Lorentz factor begin to differ noticeably from 1? What happens to the Lorentz factor as the speed of an object approaches the speed of light?
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Functions
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How fast must an object be moving if its corresponding value of $\gamma$ is to be $1.0$ percent larger than $\gamma$ is when the object is at rest? Give your answer to two significant figures.
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