WEBVTT
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This is College Physics Answers
with Shaun Dychko.
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Let's calculate gamma, the Lorentz factor,
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when we have a speed of one quarter *c*
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so we'll substitute 0.250*c*
in place of *v*.
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And so we have 1 over square root 1
minus 0.250c, all squared,
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divided by *c* squared.
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And then the *c* squared's cancel
leaving us with 0.25 squared.
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And this makes a Lorentz factor of 1.0328
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and we are allowed to keep this digit
as a significant figure
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because when we square 0.25,
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we end up with precision
to this decimal place.
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And that's the decimal place that
we'll choose in our answer here.
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So 1.0328 is our answer.
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And then in part (b), we say, suppose,
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the speed—*v*—is 0.500*c*
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and in that case, you have 1 over
square root 1 minus 0.5 squared
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which is 1.155.