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Problem 30 Medium Difficulty

A proton in a large accelerator has a kinetic energy of 175 GeV. (a) Compare this kinetic energy to the rest energy of the proton, and find an approximate expression for the proton’s kinetic energy. (b) Find the speed of the proton.

Answer

a) $\gamma m c^{2}$
b) 0.99999$c$

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Video Transcript

re noted kinetic energy Kinetic energy is a cool too Garma minus one times, uh, arrest energy. And this can be for their simply fight is gonna times e r uh, rescue nursey minus, uh, rest energy. Well, if if, uh, kinetic energy is very, very credit, then, uh, rest energy, then. Uh oh. Kinetic energy is approximately equal to gum A times M c square and no, let's find out Speed. Well, speed is equal to speed Off light times one minus one divided by Kama Square on DDE For there musical See into square root off one minus one divided by But mama can be recon is, uh, uh, kinetic energy divided by, uh, rest in Hershey. And we have square. And that's putting the values we is equal to see into screen route off one minus one. Divided by, well, kinetic energies Uh, 1 75 1 75 multiplied by 10 to the power of three, uh, divided by 930 And, uh, point tree. Ah, whole square And simplifying this we get ah, musical to zero point. Uh, line 9999 times the speed of light

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