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Problem 49 Hard Difficulty

The non relativistic expression for the momentum of a particle, $p=m v,$ can be used if $v < < c .$ For what speed does the use of this formula give an error in the momentum of (a) 1.00$\%$ and (b) 10.0$\%$ ?

Answer

a) 0.141$c$
b) 0.436$c$

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Video Transcript

well, Delta P divided by B. Well, don't be Exchange momentum and peas. Just momentum. So the racial is equal to gum. A minus one times. Mm. We divided by well, these gamma times, m we And this whole trump is equal to 1% and 1% is equal to 0.1 And the Sim Ply State gamma is equal to one divided by 0.9 mine Xeno. And since come is equal to one divided by ah screen route off one minus. Police were divided by C Square and the high is equal to 0.990 and solving. For we, we is equal to 0.1 for one times the speed of light. And also we have Don't be demanding it be, uh is equal to gamma minus one times and we divided by, uh, gonna times and we gonna times and we And it's equal to 10%. These done and 10% 10.0% is equal to unseat a 0.10 And gunmen is equal to one divided by zero point mind 00 Then gonna use one divided by a squared who does one minus we squinty body by C Square, we screened your mindedly cease creator and it's equal to one divided by zero point times zero and solving from B, we is equal to 0.436 times the speed of light.

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