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Mass and Energy in Special Relativity
 It has been shown here that the measured mass of a body depends on the velocity of the body relative to the observer making the measurement. From this it was concluded that momentum also must be a relative concept (as momentum is the product of mass and velocity). We find that the "relativistic" momentum of body can be found by simply using the Newtonian equation for momentum but with the appropriate (velocity dependent) mass. This is not the case when calculating the kinetic energy possessed by a body. Suppose we have a body of rest mass, mo which we cause to accelerate away from observer A. During the period of acceleration, work is being done by the force. As in Newtonian mechanics, we will define the kinetic energy of the body to be equal to the work done accelerating it. It can be shown that if the speed of the body relative to A is such that its mass (as measured by A) is m, then Here we are seeing the equivalence of mass and energy. Some of the work done by the force is converted into mass and if we define the total energy, E, possessed by a body to be the sum of its rest energy (moc2) and its K.E. we arrive at the most famous equation in physics It is easy to show that if the velocity of the body relative to the observer is small compared with the velocity of light, then the relativistic formula reduces to the Newtonian expression (½mv2) If the velocity of the body relative to the observer is very close to the velocity of light, virtually all the work done by the force is converted to mass. In other words... no matter how long you keep pushing the body, it doesn't go any faster! Experiments involving high speed protons, electrons etc in particle accelerators, confirm these predictions of special relativity. Units of Mass and Energy The S.I. unit for mass is the kilogram. The S.I. unit for energy is the Joule. We now see that mass and energy can be considered to be two manifestations of one underlying phenomenon (let's call it mass/energy or maybe massergy or perhaps enermass... ok, maybe not!) As discussed here, when referring to the quantities of energy possessed by sub-atomic particles, we often use the electron-Volt (eV) where 1eV = 1.6×10-19J Perhaps a little perversely, having invented this nice small unit, we then often go back the other way and use Mega-electron-Volts (MeV), where 1MeV = 1.6×10-13J So, when working with sub-atomic particles, the unit for the quantity mc2, a quantity of energy, is the MeV This then leads us to alternative unit for mass (on the small sale): If mc2 corresponds to energy then mc2/c2 corresponds to mass. For example, the energy equivalent to the rest mass of an electron (9.1×10-31kg), from E = mc2, turns out to be about 511MeV. Thus we can say that an electron has a rest energy of 511MeV and/or a rest mass of 511MeV/c2
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