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Problem 35 Medium Difficulty

Starting with the definitions of relativistic energy and momentum, show that $E^{2}=p^{2} c^{2}+m^{2} c^{4}$ (Eq. 26.13).


$E^{2}=p^{2} c^{2}+m^{2} c^{4}$


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Video Transcript

we know that he is equal to gamma times M C square A taking screen on both sides. We have e square is equal to gum square times, um, am square multiply by see to the power for and this can be returnees E square divided by C square is equal to Garma square times Mm square times C square and also we have be square is equal to guy almost greater times M squared times C square. Let's say this is a question number one. This is a question number two no subtracting you square divided by C square minus piece. Where is equal to gonna square times I'm square into one minus. Um, yeah, not one minus C C square minus C square minus. We swear. And, uh, let's, uh, simply findings for there. So the square divided by C square minus B square is equal to gonna square times m squared. I'm C Square and C squared is the common day for me and one minus B squared, divided by C square inside the bracket and therefore we have e square divided by C squared is equal to, uh, he squared, divided by C square minus minus B Square is equal to M screener C square. Look him and, uh, part there. We have ah ee Screener is equal to these were C square less am squaring to C to the dollar four.

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