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Velocity sclceto Consst electric and magnetic ficlds dcscrbed Dv the exprcssions and B waith ncarivc X-direcrlar undercctci (Notc that /40 cv rcorcscnts thc kinctic...

Question

Velocity sclceto Consst electric and magnetic ficlds dcscrbed Dv the exprcssions and B waith ncarivc X-direcrlar undercctci (Notc that /40 cv rcorcscnts thc kinctic cncrqy thc clectron, and that22.0 mi: Find thc waluc cf Kin 4M suci 602cicctron movinodo VcU derermir the speedecrronKnoykinetic energy? kvimWhat If? For the value MevToundrait (a}, what would the Klnetic enerynrorom haveMeV) formove underlecteddlrecticn}negarive

velocity sclceto Consst electric and magnetic ficlds dcscrbed Dv the exprcssions and B waith ncarivc X-direcrlar undercctci (Notc that /40 cv rcorcscnts thc kinctic cncrqy thc clectron, and that 22.0 mi: Find thc waluc cf Kin 4M suci 602 cicctron movino do VcU derermir the speed ecrron Knoy kinetic energy? kvim What If? For the value Mev Tound rait (a}, what would the Klnetic enery nrorom have MeV) for move underlected dlrecticn} negarive



Answers

The rest energy of an electron is 0.511 MeV. The rest energy of a proton is 938 MeV. Assume both particles have kinetic energies of 2.00 MeV. Find the speed of (a) the electron and (b) the proton. (c) By how much does the speed of the electron exceed that of the proton? Note: Perform the calculations in MeV; don’t convert the energies to joules. The answer is sensitive to rounding.

In this problem. First time writing they given data yet. So he had reached mass EMC squared is equal to 0.511 M E p. Also given that the speed of electron is equal to point to see, I can write the total relative which take energy of the electron is equal to gamma M C square which is equal to EMC square by Under Hood one minus U squared by c square which is equal to one by under route one minus point to see Holy square by c square. Multiplication 0.511 M E p which is equal to 0.5-1 pipe to D M E B. Now going forward and calculating the relativistic kinetic energy which is given by Ikea is equal to gamma EMC squared minus EMC squared which is equal to one by under Hood 1 -1 you is squared by C Squared -1. Multiplication. EMC squared. Which one simplification and I can be expressed in age one by under Hood 1 -1 point to see. Holy Square by C. -1. On solving it. Further multiplication .511 MDB. So for the simplification I can write the expression has won by Underwood one minus point. You're a four -1 multiplication .511 mm P. So solving it further, I can write the value of EK. is equal to 1.0 206 to 0 minus one. Multiplication 10.511 M E P Which is equal 2.010 5:37 MEP. Now the relativistic moment of the electron is given by P is equal to M U P is equal to M U. Bye. Under one minus U squared by c square On further simplification I can write devalue AP is equal to .5.1 MDB by c squared. Multiplication point to see by under hood one minus point to see. Holy squared by C square. Which one simplification? I get devaluate 10.11 mdb by sea, multiplication. Point to Point to buy under 1 -14. So on. Further solving I finally get the value of P is equal to 0.10 both the Emmy bi bi si as the answer.

An electron is moving with a kinetic energy of 1.264 mega electron volts. What is it speed? So we know the total energy is the kinetic energy plus the rest mass energy. So this is since the kinetic energy It's 1.264 mega electron volts, And the rest mass energy is 0.511 mega electron volts. This gives us a total energy of 1.775 mega electron volts. So using equation 36 and rewriting it for V, we get C times the squared of one minus EMC squared squared over e squared. So, plugging in our values and we get 0.958 c.

In this exercise, we have information that the rest energy of the election is equal to 0.511 may like from books, while the rest energy of the Crowton is equal to on 138 Megatron votes. And I have to assume that the kinetic energy of both particles is equal to two Megatron votes in question. A. We have to find what is the speed of the So first, remember that the kinetic energy is equal to the total energy. Mine is the rest energy of the particle. Then I'm just gonna call the zero. Because here I'm working with a general particle. Remember that E the total energy is equal. Chew, go! What times the rest Energy. So K is equal to gamma times. The rest center, you might as the rest enter you. So this is gonna miners one times the rest energy So K over the zero plus one is equal to go. I remember that gamma is one over the square root of one minus B squared over C squared. So one minus B squared over C squared is equal to one over WAM plus k over easier. All of this square. So that's isolate V. In order to find the function off K and the rest energy of the particles have one minus one over, uh, one plus K over a zero square. And this is equal to these were overseas square, So V is equal to the square root of one minus one over Won't les que over he zero Where time See, for the electric we have a feasible to 11 is one over one plus two mag electoral votes divided by 0.511 mega let from boots squared time See? So this is it which is your 0.98 times. See the question be, we have to repeat it for the protein. So I'm just gonna use the final former that I derived in Question A And instead of subsisting the rest energy of the electron, I'm gonna sifted through the rest Inter year of the protein. So V is equal to the square root of Juan minus one over one plus two Megatron votes divided by 900 in 38. Make electoral vote swear. I'm see, this is equal to 0.65 times. See in question see, I have to find the difference between the speed of the electorate and the speed of the protein s O. This is just the E. That's this bit of black electron minus VP. That's in speed of the proton. This is nine as urban 98 C minus 0.65 c. So this is your 0.915 times the speed of light, See, and in question, Do you have to repeat the less three items? But with magnetic energy of 2000? May I from foods. So basically, I'm gonna go back to the equation that I'd arrived in question A and just substitute K, uh, as 2000 mega rectangles. So for the speed of the electric, this is equal to one miners, one over one plus 2000. The writer by the Mass, uh, the rest energy of the Election Square. See, this is equal to zero point 9999 and 99 times this beautiful lights he and then So this is the speed of the electorate. And then, for the speed of the proton is equal to the square root of one. Mine is one over one plus 2000 mega convulsive out of 8 900 and 38 Mega from Boots Square, I'm see. So this is equal to zero point 948 times the speed of light, See? And the difference between Ah the to the man is V P is equal to 0.52 times. It's been a lot which concludes our exorcists.

Well, look, something we're talking about. Speed of fast moving hurdled. So her They were absent from a speeding particle. Well, six million Trumbull. That's a protein on that zoonotic country in the past. For the rest, energy of protest. Just give us by for three eight 0.3 million electron volts. So, Chairman, I don't see square is equal to okay. Plus, I'm too square. That makes 1/1 minus piece where she square people to. Okay, over time she squared plus one. So that would be just one financed corn because of our Okay, um, C square was one pull over square and then the square root of everything I see. And that goes looking at our members swear right of one mineards one blighted by two 930. If you quit three plus one. All that's where times Three times. Thanks. Power back. You just But we lost three. 24 seven meters per second. So a little more than attempt of this beautiful so party were asked to solve the same What type of problem, but all right, to make a little trouble. That is gonna be, uh, Culio matter. And the the rest energy of a feeling, um, is equal to 3000 728. They get electron Bull, so B is equal to Let's just like it on Earth, since we are resolved for a little party bond minor one divided by 20 divided by way 37 28 Find it or plus one that quantity square times. Three, However, be people to 3.1 times 10 70 per second. Also about the type of dispute of life next, or give it a velocity and a kinetic energy and asked to figure out what will it is. So C is equal to perceived, but we one or pillow are trouble and the loftiest to cancel seven. There's per second. Yeah, People's Square. Yeah, given C squared equals K. Plus, I'm c squared before I'm xi squared equals Okay, but if I can finest one is equal to 1.14 Kill all our trouble rules about by the square root or right I one over the square root performed the minor to founded by 30. I swear, I just cancelled out the How are you talking? But it's one people 0.511 mega Look troubled. And that's equivalents of the president. Feel an electron. Soon we have to recap 3.4 times 10 with seven meters percent Party for part B. We, uh, 3.1 times 10 with 70 meters per second and or part C. You have a lot of trust and love, Thanks.


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