What is the momentum of the
proton? Its mass is 1.67×10í^27
kg.
p = 2.89×10í^19 kg·m/s
(Relativistic effects add 15%)
35.12 - Mass and energy
The world’s “most famous equation” is shown in Equation 1: Rest energy (also known
asmass energy) equals mass times the speed of light squared. By “rest energy”, we
mean the energy equivalent of its mass.
If a mass is moving, its total relativistic energy can be calculated as the sum of this
value and its kinetic energy. The equation for calculating this total energy is shown in
Equation 2. The equation factors in relativistic effects when calculating KE.
It is interesting to consider Equation 1 in the context of the Sun. The Sun becomes less
massive as its mass is transformed by fusion reactions into the energy it radiates. It
radiates 3.91×10^26 joules of energy per second, and as a consequence, it “loses” more
than four billion kilograms per second! (But do not worry! Its total mass is 1.99×10^30 kg).
Earlier scientists had proposed the conservation of mass in chemical reactions. This
textbook has discussed the conservation of energy. At non-relativistic speeds, these
principles hold true to a high degree of accuracy. Einstein showed both mass and
energy must be considered when applying conservation principles.
Thermonuclear processes inside the sun convert a very large quantity of mass into a
stupendous quantity of energy every second. Much more comprehensible amounts of
matter yield tremendous amounts of energy as well. For example, if one gram of matter
were converted entirely to energy, it would produce the energy equivalent of
combusting fifteen thousand barrels of oil. On the dark side of things, converting into
energy a tiny fraction of the 2 kg of matter in a nuclear bomb can produce a blast
equivalent to the chemical energy released from the explosion of 50 billion kilograms of
dynamite.
Atomic particles are often subject to relativistic effects because of their high speeds. For convenience, the energy and mass of such particles is
often measured in units other than joules and kilograms. An electron volt (eV) equals the change in the potential energy of an elementary
charge (1.60×10í^19 C) when it moves through a potential difference of one volt. Electron volts are convenient measures of particle energy.
Particle mass is often measured in units of eV/c^2 , or energy divided by the speed of light squared. The fact that these are mass units follows
from the equation E = mc^2.Energy at rest
E 0 = mc^2
E 0 = rest energy
m = mass
c = speed of light
(^652) Copyright 2007 Kinetic Books Co. Chapter 35