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$\bullet$ (a) Through what potential difference does an electronhave to be accelerated, starting from rest, to achieve a speed of0.980$c ?$ (b) What is the kinetic energy of the electron at thisspeed? Express your answer in joules and in electronvolts.

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$=3.30 \times 10^{-13} \mathrm{J}$

Physics 101 Mechanics

Chapter 27

Relativity

Gravitation

Cornell University

Simon Fraser University

University of Winnipeg

Lectures

03:55

In physics, orbital motion is the motion of an object around another object, which is often a star or planet. Orbital motion is affected by the gravity of the central object, as well as by the resistance of deep space (which is negligible at the distances of most orbits in the Solar System).

03:18

Sir Isaac Newton described the law of universal gravitation in his work "Philosophiæ Naturalis Principia Mathematica" (1687). The law states that every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them.

01:37

(a) Through what potential…

03:56

Part A:Through what po…

02:41

An electron has been accel…

09:07

An electron is accelerated…

02:15

Through what potential dif…

01:06

Suppose an electron is acc…

01:02

06:01

02:17

(a) What potential differe…

So it's starting from rest, which means initial velocity zero. We want to accelerate electro. So a speed off zero point 98 seat by a difference in difference of putting show. So we want to increase the energy off electric in this case, the connecting energy because he has the speed by a difference in potential. So this is just the charge of the electron times the difference in potential. So this is the creation that we have to use. So first of all, in the first item, we want to calculate, I turn a we want to calculate what should be the difference in pretension. I can be. We want to calculate what should be the absolute value off the connecting energy off the electron. So first of all, we do not have any ways to calculate the difference in potential in first. So let's calculate the connecting energy because it's easier. We know by definition that the connective relativistic energy is just gamma M C square minus M c square, so we can see that the connecting Aaron and you relativistic energy is just m C square. There multiplies gamma minus one. So we just have to calculate gamma and then calculate M C Square and we'll be fine. So this is just let's see and see square. We know that it's this one one minus 0.98 See, divided by sea square in the square root so we can cross, see and hear minus one. So this is the connecting energy one miners, you don't buy 98 here we know the mass of the electron We know the speed of light. So this is just the connecting energy is just four point 0 25 m c. Square. So this is just equal two three point 95 2 95 actually 2 95 times 10 to the power of minors, 13 jowls or we can see in the electoral votes. This is two points, you know, six lev because to convert jowls to a lateral votes, we just have to multiply by six points two for two time stand to the power off 18. So this is value off the connecting energy off the electron. So now that we have the connecting energy of the electron, we can finally calculate the difference in potential that is necessary. So the difference of potential. It should be out of e e close the connecting energy divided by the charge of the electron. So this is simply 2.6 times 10 to the power off six votes. Just remember that the connecting energy that we years in is that three point 2 95 time Stan, our miners 13. So as we can see the value off, the difference in potential is just the energy in electoral votes is closed to damage of electoral votes because here we have Mager, he would have Maga. And here we have 10 to the power of six. So it's pretty goes, but it's not equal. So this is the final answer to the problem. The first answer, the answer to the value of the connecting energy is 3.2 95 Time stand to the power of minors 13 and the value of the difference in potential is this one. And here this is a different potential. And that's all. Thanks for watching

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