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10. In Einstein's theory of special relativity, the kinetic energy of a particle is written as $E_k = \frac{mc^2}{\sqrt{1-(v/c)^2}} - mc^2$ and the total energy of a particle can be written as $E_t^2 = p^2c^2 + (mc^2)^2$ where m is the particle rest mass, c is the speed of light, and v is the velocity of the particle. In this course, we will consider energy of moving objects with $v << c$ (e.g., in a wind turbine or automobile) as well as energetic particles (photons) moving at effectively the speed of light (incident solar energy). Using these equations as needed, find the expressions for kinetic energy when a) $v << c$ b) $v = c$ (i.e., a photon) You may need to remember some expansions from your math classes.

          10. In Einstein's theory of special relativity, the kinetic energy of a particle is written as
$E_k = \frac{mc^2}{\sqrt{1-(v/c)^2}} - mc^2$
and the total energy of a particle can be written as
$E_t^2 = p^2c^2 + (mc^2)^2$
where m is the particle rest mass, c is the speed of light, and v is the velocity of the particle. In this course,
we will consider energy of moving objects with $v << c$ (e.g., in a wind turbine or automobile) as well as
energetic particles (photons) moving at effectively the speed of light (incident solar energy).
Using these equations as needed, find the expressions for kinetic energy when
a) $v << c$
b) $v = c$ (i.e., a photon)
You may need to remember some expansions from your math classes.

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10. In Einstein's theory of special relativity, the kinetic energy of a particle is written as
Ek = (mc^2)/(√(1-(v/c)^2)) - mc^2
and the total energy of a particle can be written as
Et^2 = p^2c^2 + (mc^2)^2
where m is the particle rest mass, c is the speed of light, and v is the velocity of the particle. In this course,
we will consider energy of moving objects with v << c (e.g., in a wind turbine or automobile) as well as
energetic particles (photons) moving at effectively the speed of light (incident solar energy).
Using these equations as needed, find the expressions for kinetic energy when
a) v << c
b) v = c (i.e., a photon)
You may need to remember some expansions from your math classes.

Added by Brenda L.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Timothy James

05/08/2022

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Therefore, we can use a Taylor series expansion to approximate the expression for kinetic energy. Show more…

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I need help. I do not know how to solve these problems. It is in the topic of waves and light in the book of physics of energy. Please help me :) 10. In Einstein's theory of special relativity, the kinetic energy of a particle is written as: E = me? - mc^2 / (1 - v/c) And the total energy of a particle can be written as: E = pc + mc^2 / 2 Where m is the particle rest mass, c is the speed of light, and v is the velocity of the particle. In this course, we will consider the energy of moving objects with v << c (e.g., in a wind turbine or automobile) as well as energetic particles (photons) moving at effectively the speed of light (incident solar energy). Using these equations as needed, find the expressions for kinetic energy when: a) v << c b) v = c (i.e., a photon) You may need to remember some expansions from your math classes.

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00:01 So we're calculating a couple of things about an electron, given that it's got a wave number of 50 inverse nanometers.

00:12 And the first thing we want to calculate is the debroy wavelength of this electron in meters.

00:18 And so by definition, the wavelength is like 2 pi over the wave number.

00:23 And so if we do that, this is going to be like pi over 25, right, 2.

00:30 Pi over 50s, pi over 25 nanometers.

00:33 And of course, we have to convert this to meters.

00:35 So this would just be pi over 25 times 10 to the negative 9 meters.

00:44 And of course, if you want to do pi over 25, you get, you get 0 .125, something's, so like 1 .25, 1 .26 times 10 to the negative 10 meters.

00:58 So that's our wavelength.

01:01 Next, we're calculating the momentum of this electron.

01:04 So there are a couple ways to do this.

01:06 One is that you can write the momentum as p equals plank's reduced constant times the wave number.

01:15 Planks reduce constant, you're not familiar with.

01:18 It is the ordinary planks constant divided by 2 pi.

01:21 And this is fine because we already have the wave number.

01:24 So it turns out plank's reduce constant is about 6 .3.

01:28 Five, eight times 10 to the negative 16th electron volt seconds.

01:36 We're told to use electron volts per unit c, per speed of light...

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