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Numerade Educator



Problem 15 Medium Difficulty

(a) What is the momentum of a proton moving at 0.900$c$?
(b) At what speed will a particle’s relativistic momentum equal twice its classical momentum?


a) $1.03 \times 10^{-18} \mathrm{~kg} \mathrm{~ms}-1$
b) $2.60 \times 10^{8} \mathrm{~m} / \mathrm{s}$


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Ashutosh K.

November 19, 2020

Video Transcript

we know that speed of proton. Ah, speed, speed or proton Speed off proton. We is equal to the seed of find 900 times the speed of light and massive proton and not physical too. 1167 multiplied by, uh, 10 to the power minus 27 kilogram. Now let's do party. We need to find a lead with stick Memento. And we know that relativistic momentum p is equal to and not times we divided by, uh square Rudolph one minus we square divided by C square and therefore momentum relativistic momentum musical to him Not him, not his 1.67 multiply returned to the parlor minus 27. Multiply the speed of proton Speed off down zero point line 00 times See and C is three. Multiply by 10 to the power it divided by divided by ah, square root square root off one minus Well, we is 0.900 time. See whole square divided by C square. Okay. And this gives this well solving this We get one point 03 Multiply by 10 to the power minus 18 kilogram minus 18 kilogram later or second. Okay, No. Let's new part B Here we will do part B, part B. Well, according to given condition, logistic momentum is two times off. Classical woman, too. Classical momento. They know that logistic momentum is am not times we divided by square root off one minus we squared, divided by C square Classical momentum is Justin, not times we now we need to solve for weeks. So we will sold for me. So this can be returnees, uh, and not gets cancelled from both sides. And we have a re square divided by, uh C square minus B square divided by C square is equal to four dimes. Four dimes off we square we square. And for there we have ah ah C square divided by C squared minus. We square is equal to four and this can be written It C squared is equal to, um four four into or four C squared minus for we square. And we have ah c squared minus four. Seas were is equal to minus. Won't be square and see Squeeze common. We have one minus four inside wreckage physical too minus for we square. And we have minus three. C square is equal to minus 43 square minus kit gets cancelled minus and taking a screen route on both sides. We have to go, wrote three times. He's equal to two times we and B is equal to a tree divided by two times the speed of light and putting the values, putting the value speed of light, putting the value of C. But we have to find six, 2.60 multiplied by 10 to the Power Kid major for a second.

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