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$\bullet$ Electrons are accelerated through a potential difference of$750 \mathrm{kV},$ so that their kinetic energy is $7.50 \times 10^{5} \mathrm{eV}$ . (a) Whatis the ratio of the speed $v$ of an electron having this energy tothe speed of light, $c ?$ (b) What would the speed be if it werecomputed from the principles of classical mechanics?

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$$= \longdiv { 5 . 1 3 \times 1 0 ^ { 8 } \mathrm { m } / \mathrm { s } }$$

Physics 101 Mechanics

Chapter 27

Relativity

Gravitation

Cornell University

Hope College

University of Sheffield

McMaster University

Lectures

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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).

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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.

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Electrons are accelerated …

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(a) Through what potential…

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An electron has been accel…

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(a) What potential differe…

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An electron is accelerated…

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in part a of this problem. We're given the kinetic energy of a gn electron, and we want to know how fast it's going. And the kinetic energy is given to us in units of evey 7.5 times 10 to the five evey. So the first thing we want to do is convert this to Jules, using 1.6 times 10 to the negative 19 Jules Previ And what we get is that the kinetic energy is 1.2 times 10 to the negative 13. Jules, keep in mind is well that the mass of an electron is 9.11 times 10 to the negative 31 kilograms, and the kinetic energy in relativity is M C squared times gamma minus one. So if we saw this for gamma, we get, um, that it's equal to K over M c squared plus one. And this is an equation that can be solved for V. And if you do the algebra carefully, what you should find is that me is equal to 0.914 C now, in part B, um, we were asked what the velocity would be non relativistic Lee suites at 1/2 and B squared equals two. The same kinetic energy. I 1.2 temps in the negative 13 Jules and I'm solving this for V gives that it's 5.13 times 10 to the eight meters per second, which would be greater than the speed of light, and relativity says that that's impossible.

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