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Question
Find the momentum of a helium nucleus having a mass of $6.68 \times 10^{-27} \textrm{ kg}$ that is moving at $0.200c$.
Question by OpenStax is licensed under CC BY 4.0.
Final Answer
$4.09 \times 10^{-19} \textrm{ kg} \cdot \textrm{m/s}$
Solution Video

OpenStax College Physics Solution, Chapter 28, Problem 35 (Problems & Exercises) (1:05)

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Video Transcript

This is College Physics Answers with Shaun Dychko. This helium nucleus has a mass of 6.68 times 10 to the minus 27 kilograms and has a velocity of 0.200<i>c</i>. And we want to know its relativistic momentum, which is the Lorentz factor times its mass times its velocity. And so that's gonna be <i>mu</i> over the square root of 1 minus— I should put a <i>u</i> here because that's the letter we are using for velocity in this question— <i>u</i> squared over <i>c</i> squared. So we have <i>m</i> times 0.200<i>c</i>, which is the velocity, divided by square root of 1 minus 0.200<i>c</i> squared over <i>c</i> squared. And the <i>c</i> squared's cancel and we have <i>m</i> times 0.200<i>c</i> over square root 1 minus 0.200 squared. Then we can plug in the mass of the Helium nucleus— 6.68 times 10 to the minus 27 kilograms— multiply it by 0.200 and then multiply it by the speed of light and divide by the square root of 1 minus 0.2 squared. And this gives a momentum of 4.09 times 10 to the minus 19 kilograms meters per second.