Relativistic Momentum and EnergyRelativistic Momentum (p)It is just classical momentum multiplied by the relativistic factor (y).4.0-2 3.0-p = ymu2.0-where m is the rest mass of the object, u is its velocity relative to an observer,and the relativistic factor.1.0-1Y =0-0.2c 0.4c 0.6c 0.8c 1.0cRelativistic momentum has the same intuitive feel as classical momentum.speed u (m/s)It is greatest for large masses moving at high velocities, but, because of thefactor (7), relativistic momentum approaches infinity as velocity (u)Figure 1. Relativistic momentumapproaches infinity as the velocity ofan object approaches the speed oflight.approaches speed of light (c). (See Figure 1) This is another indication thatan object with mass cannot reach the speed of light. If it did, its momentumwould become infinite, an unreasonable value.Example:An electron, which has a mass of 9.11 x 10-31 kg, moves with a speed of 0.750c. Find its relativistic momentum.Given:Solution:me = 9.11 x 1031 kgu = 0.750cmeu(9.11 x 10-31 kg)(0.750)(3.00 x 108 m/s)p =3.10 x 1022 kgm/s/1-(0.750c)²c2u2Relativistic EnergyThe first postulate of relativity states that the laws of physics are the same in all inertial frames. Einstein showedthat the law of conservation of energy is valid relativistically, if we define energy to include a relativistic factor. Itcan be summarized by the equation below:Total Energy (E)is defined as:Kinetic Energy (K)is defined as:K = ymc²- mc²Rest Energy Energy (Eo)is defined as:%3DE = ymc²E, = mc²The Relationship of relativistic momentum and energy can be defined by:E = (pc) + (mc²)²Example:An electron in a television picture tube typically moves with a speed u = 0.25c. Find its total energy and kineticenergy in electron volts (Eo = 0.511 MeV).Given:Solution:Eo = 0.511 MeVmęc2Eo0.511 MeVu = 0.25cE == 0.528 MeyK= E- Eo = 0.528 MeV – 0.511 MeVu2(0.25c)2|0.017 MeVActivity:Solve the following problems. Use the rubrics as your guide in presenting your solution (refer to attachment A.1at the next page).1. An electron, which has a mass of 8.45 x 10-31 kg, moves with a speed of 0.45c. Find its relativisticmomentum and find the percentage increase of its relativistic momentum from its classical momentum.2. An electron in a television picture tube typically moves with a speed u = 0.25c. Find its total energy andkinetic energy in electron volts (Eo = 0.385 MeV)momentum Prel (kg m/s)

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An electron, which has a mass of 8.45 x 10-31 kg, moves with a speed of 0.45c. Find its relativistic momentum and find the percentage increase of its relativistic momentum from its classical momentum. An electron in a television picture tube typically moves with a speed u = 0.25c. Find its total energy and kinetic energy in electron volts (Eo = 0.385 MeV)

An electron, which has a mass of 8.45 x 10-31 kg, moves with a speed of 0.45c. Find its relativistic momentum and find the percentage increase of its relativistic momentum from its classical momentum. An electron in a television picture tube typically moves with a speed u = 0.25c. Find its total energy and kinetic energy in electron volts (Eo = 0.385 MeV)

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter28: Special Relativity

Section: Chapter Questions

Problem 72PE: Construct Your Own Problem Consider an astronaut traveling to another star at a relativistic...

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