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)

Answered: Image /qna-images/answer/a0a4d44b-c9dd-456e-823a-ecf7e4b5eab5.jpg

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

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

An unstable particle with a mass equal to 3.34 ✕ 10−27 kg is initially at rest. The particle decays into two fragments that fly off with velocities of 0.981c and −0.861c, respectively. Find the masses of the fragments in kg. (Hint: Conserve both mass–energy and momentum.)
An elementary particle of mass 9.5 x 10-27 kg is moving at speed 9 x 107 m/s. (A) Its relativistic momentum in terms of its classical momentum (B) Its KE = . (C) Its rest energy = . (D) Its total energy
Starting with the definitions of relativistic energy and momentum, show that E2 =P2c2 +m2c4 (Eq. 26.13).
Particle A has a rest energy of 1192 MeV and is moving through the laboratory in the positive x direction with a speed of 0.450c. It decays into particle B (rest energy = 1116 MeV) and a photon; particle A disappears in the decay process. Particle B moves at a speed of 0.400c at an angle of 3.03° with the positive x axis. The photon moves in a direction at an angle with the positive x axis. A 0.45c What are the 0.40c photon Ө 3.03⁰ B in MeVs and your answer in three significant digits. in degrees of the photon? Give
Compute the kinetic energy of a proton (mass 1.67 x 10-27 kg) using both the nonrelativis- tic and relativistic expressions (a) 8.0 x 107 m/s and (b) 2.858 m/s
The half‑life of a certain subatomic particle at rest is about 1.00×10−8 s. With what speed V is a beam of these particles moving if one‑half of them decay in 4.00×10−8 s as measured in the laboratory? V = ? m/s
Consider a proton that has a momentum of 1.00 kg·m/s. Part (a) Calculate the relativistic parameter γ for the proton. You will have to use a 2.998 × 108 for the speed of light to get this answer correct. Part (b) What is its speed, in meters per second? Such protons form a rare component of cosmic radiation with uncertain origins.
Calculate the ratio of the relativistic kinetic energy to the classical energy kinetic energy for an electron (mass = 9.109x10^-31 kg) moving with constant speed of 0.75c.
A particle has a rest energy of 4.31×10−13 J and a total energy of 8.33×10−13 J. Calculate the momentum p of the particle.
An electron is moving with a kinetic energy of 0.923 MeV.What is its speed?
A rocket is traveling through space and its Lorentz factor (y) is 3.9. Determine the rocket's speed (in terms of c) and the ratio of its kinetic energy to its total energy. V= ? X c KE/E= ?