# What is energy momentum relation 1

## Physics compact, basic knowledge 8, textbook

25 20.5 Equivalence of energy and mass Energy and momentum A1 Derive a relationship between kinetic energy and momentum in the context of classical mechanics! The aim of this section is to derive and interpret a relativistic connection between energy and momentum. We start from the speed dependence of the mass: m c v m 1 0 2 2 0 = - (1) Using the equations for the total energy and the momentum E = m. c 0 2 and p = m. v is obtained from (1) through elementary transformations the A2 calculation! The relativistic energy-momentum relation allows some remarkable conclusions. The momentum of photons Photons are particles that move at the speed of light. Therefore they must not have a rest mass (m 0 = 0). For photons the relativistic E-p relation is simplified to: E = p. c 0 It results from this together with E = h. f and c = m. f the A3 rake! Interpretation: Photons have an impulse that is inversely proportional to the wavelength of the light. When photons interact with matter, we expect not only an exchange of energy but also a transfer of momentum. 20.5.2 20.5.3 3. The following values for the speed of the balls result for system I: Ball A: v A = Y / T v A… speed of ball A in IY… travel in y-direction T… time in system I The ball B moves in system I with the (great) speed v. Therefore, when calculating the speed v B, the time dilation must be taken into account: v TY cv 1 B 0 2 2 $ = - - v B… speed of the ball B in I in y direction Y… travel in y direction v… Speed of the ball B in the x direction c 0… the speed of light in a vacuum T… time in system I 4. In system I, the law of conservation of momentum must apply. Before the collision, the momentum in y direction is zero. Therefore, the momentum of the balls in the y -direction must also be zero after the impact: p A + p B = 0 m A. v A + m B. v B = 0 p A… momentum of ball A in y direction p B… momentum of ball B in y direction m A… mass of ball A in I: m A = m 0, because A in I moves only slowly v A… speed of ball A in I in y direction m B… mass of ball B, which is moving at high speed v in x direction v B… speed of ball B in I in y direction Insertion of the expression for v B in the law of conservation of momentum yields: mmcv 1 AB 0 2 2 $ = - Since m A is the mass of a ball (almost) at rest and m B is the mass of a similar, rapidly moving ball, one can use m A with of rest mass m 0 and m B with (dynamic) mass m. This leads to the formula mcvm 1 0 2 2 0 = - m… (dynamic) mass m 0… rest mass v… speed c 0… speed of light in vacuum E 2 = m 0 2. c 0 4 + p 2. c 0 2 E… total energy m 0… rest mass c 0… vacuum speed of light p… (relativistic) momentum Relativistic energy-momentum relation p = h / mp… momentum of a photon h… Planck's quantum of action m… wavelength momentum of a photon For test purposes only - property of the publisher öbv

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