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Proton moves with a speed of 0.950c through a laboratory: (a) Calculate the total energy of the proton in the laboratory frame_ (b) Calculate the kinetic energy of ...

Question

Proton moves with a speed of 0.950c through a laboratory: (a) Calculate the total energy of the proton in the laboratory frame_ (b) Calculate the kinetic energy of the proton in the laboratory frame Give your answers in mega electron volts_

proton moves with a speed of 0.950c through a laboratory: (a) Calculate the total energy of the proton in the laboratory frame_ (b) Calculate the kinetic energy of the proton in the laboratory frame Give your answers in mega electron volts_



Answers

A proton moves at 0.950c. Calculate its (a) rest energy, (b) total energy, and (c) kinetic energy.

In this question were given the value of bitter for a proton, which is equal to Be to equal to 0.95. We have to calculate the corresponding relativistic total energy and momentum of the proton. We know that the relativistic total energy can be written as the mass of a proton into C square, divided by square root of one minus vita square. So this mp into c squared in billion electron volts can be written as 0.9382 billion electron volt divided by the square root of one minus B squared 0.995. That square. So simplification of this equation will give us the head of energy or the total energy of the proton as 9.38 billion electron. 4th. So this is the answer for the first part of the equation. In second part where to find the relativistic momentum of the proton. So for a second part we can just try it. The previous one is the the first part. This is first part for relativistic moment. And we can write p times see as equal to square out of is square minus M p c square hole square. So we've got the value of E as 9.38 billion electrical. So that would put 9.38 square minus MPC. Is can we already know that is 0.9382 billion electrical. That square. So this will give us the value of pc As he called a 9.3 or four Billion electron volt are the momentum of the protein will be equal to 9.34 billion electron for by sea. So this is the required value of relativistic momentum of the proton.

Remember that force equals mass times acceleration and for charges, it is Q times E. So from here we were there. Acceleration equals que e over em. So now we know that it is accelerated by 120 Voltage 120 volt charges one for six times 10 to the native nine deal divided by the mass Using mass for proton equals 1.67 time. Stand to the negative 27 k g for massif In electron, this number is 9.1 times 10 to the negative 27 kilogram. Using this acceleration for the proton comes out to be 152 triple zero meters per second or 1 52 is the meter for a second. From here we get acceleration for the electron ese 6.49 times tend to their six meters per second.

For this problem on the topic of electric potential, we want to calculate the speed of a proton as well as the speed of an electron that is accelerated through A potential difference from rest of 120 balls. Now the energy of the proton field system is conserved as the proton moves from high to low potential. Which can be defined for this problem as moving from 120 balls down to zero walls. So by applying the conservation of energy, we have the initial kinetic energy of the proton plus its initial potential energy plus any work done against resistance forces down to E. Is equal to the final kinetic energy plus the final electric potential energy. So we know initially it only has electric potential energy. So zero plus Q. V. That's zero is equal to the final kinetic energy of the proton, which is a half M Vp squid. And so that means the charge of the proton 1.6 times 10 to the minus 19 Columns times a potential difference of 100 and 20 volts is equal to a half times the mass of the proton, 1.67 Times 10 to the -27 kg times the speed of the proton squared V P squared. So we can rearrange this equation since we have only one unknown and solve for VP, we get the speed of the proton to be one 0.52 Times 10 to the power of five m the second. Now we want to do the same for an electron through the same potential difference. So the electoral will gain speed in moving the other way From V. A. is equal to 02 via physical 220 balls. So again applying the conservation of energy, the kinetic energy plus the initial that electric potential energy less any welcome. And delta E. Is equal to the final kinetic energy plus the final electric potential energy. So initially the electron has no energy and finally it has kinetic energy a half M. The E squared plus Q times V. and so simply zero is equal to half times the mass of the electron. 9.11 Times 10 to the minus 31 kg times its speed squared, V squared Plus is charged -1.6 Times 10 to the minus 19 columns Times the potential difference of 120V or 120 jewels Bakula. So rearranging this equation, we get ve the speed of the electron to be six point 49 Times 10 to the power six meters per second.

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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