# Relativity

## A New Look at Energy Sample Problem

(It) What is the total energy E of a 2.53 MeV electron? SOLUTION:he KeyIdea here is that, from Eq, 38-44, the total energy E is the sum of the electron’s mass energy (or rest energy) IIIC~ and its kinetic energy: E = 0.511 MeV + 2.53 MeV =»3.04 MeV. (Answer) ib) What is the magnitude …

## Momentum and Kinetic energy

Momentum and Kinetic energy In classical mechanics. the momentum p of a particle is nil’ and its kinetic energy K is !m\,2. If we eliminate r between these two expressions, we find a direct relation between momentum and kinetic energy: p2 = 2Km We can find a similar connection in relativity by eliminating . between the relativistic definition …

## Total Energy

Total Energy Equation 38-40 gives an object’s mass energy (or rest energy) Eo that is associated with the object’s mass m, regardless of whether the object is at rest or moving. If the object is moving, it has additional energy in the form of kinetic energy K. If we  assume that its potential energy is zero, then …

## A New Look at Energy

A New Look at Energy Mass-energy The science of chemistry was initially developed with the assumption that in chemical reactions, energy and mass are conserved separately. In 1905, Einstein showed that as a consequence of his theory of special relativity, mass can be considered to  be another form of energy. Thus, the law of conservation of energy …

## A New Look at Momentum

A New Look at Momentum Suppose that a number of observers, each in a different inertial reference frame, watch an isolated collision between two particles. In classical mechanics, we have  seen that-even though the observers measure different velocities for the colliding  particles-they all find that the law of conservation of momentum holds. That is.they find that …

## Transverse Doppler Effect

Transverse Doppler Effect So far, we have discussed the Doppler effect, here and in Chapter 18, only for situations in which the source and the detector move either directly toward or directly away from each other. Figure 38-12 shows a different arrangement. in which a source  S moves past a detector D. When S reaches point P, …

## Doppler Effect for Light

Doppler Effect for Light In Section 18-8 we discussed the Doppler effect (a shift in detected frequency) for sound waves traveling in air. For such waves, the Doppler effect depends on two velocities–namely, the velocities of the source and detector with respect to the air.  (Air is the medium that transmits the waves.)That is not the situation …

## The Relativity of Velocities

The Relativity of Velocities Here we wish to use the Lorentz transformation equations to compare the velocities that two observers in different inertial reference frames S and S’ would measure for the same moving particle. Let S’ move with velocity v relative to S. Suppose that the particle, moving with constant velocity parallel to the x and …

## Time Dilation

Time Dilation Suppose now that two events occur at the same place in S’ (so .1x’ = 0) but at different times (so .1(‘ “* 0). Equation 38-22 then reduces to     This confirms time dilation. Because the two events occur at the same place in S’, the time interval t!.(‘ between them can be measured …

## Some Consequences of the Lorentz Equations

Some Consequences of the Lorentz Equations  Here we use the transformation equations of Table 38-2 to affirm some  of the conclusions that we reached earlier by arguments based directly on the postulates.       If two events occur at different places in reference frame S’ of Fig. 38-9, then t!.x’ in this equation is not zero. …