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8.4 Mass and Energy 251

QUESTION 2: You fire a bullet from a rifle.The increase of kinetic energy of the bullet
upon firing must be accompanied by a decrease of some other kind of energy. What
energy decreases?
QUESTION 3: A truck travels at constant speed down a road leading from a mountain
peak to a valley. What happens to the gravitational potential energy of the truck? How
is it dissipated?
QUESTION 4: When you apply the brakes and stop a moving automobile, what hap-
pens to the kinetic energy?
(A) Kinetic energy is converted to gravitational potential energy.
(B) Kinetic energy is converted to elastic potential energy.
(C) Kinetic energy is converted to heat due to frictional forces.
(D) Kinetic energy is converted to chemical energy.

8.4 MASS AND ENERGY

One of the great discoveries made by Albert Einstein early in the twentieth century is
that energy can be transformed into mass, and mass can be transformed into energy.
Thus, mass is a form of energy. The amount of energy contained in an amount m of
mass is given by Einstein’s famous formula

2
E mc (8.30) energy–mass relation
8
where c is the speed of light, c 3.00 10 m/s. This formula is a consequence of
Einstein’s relativistic physics. It cannot be obtained from Newton’s physics, and its
theoretical justification will have to wait until we study the theory of relativity in
Chapter 36.
The most spectacular demonstration of Einstein’s mass–energy formula is found
in the annihilation of matter and antimatter (as we will see in Chapter 41, particles of
antimatter are similar to the particles of ordinary matter, except that they have opposite
electric charge). If a proton collides with an antiproton, or an electron with an anti-
electron, the two colliding particles react violently, and they annihilate each other in
an explosion that generates an intense flash of very energetic light. According to Eq.
(8.30), the annihilation of just 1000 kg of matter and antimatter (500 kg of each)
would release an amount of energy

2
8
2
19
E mc 1000 kg (3.00 10 m/s) 9.0 10 J (8.31)
This is enough energy to satisfy the requirements of the United States for a full year.
Unfortunately, antimatter is not readily available in large amounts. On Earth, antipar-
ticles can be obtained only from reactions induced by the impact of beams of high-
energy particles on a target. These collisions occasionally result in the creation of a
particle–antiparticle pair. Such pair creation is the reverse of pair annihilation. The
creation process transforms some of the kinetic energy of the collision into mass, and
a subsequent annihilation merely gives back the original energy.
But the relationship between energy and mass in Eq. (8.30) also has another aspect.
Energy has mass. Whenever the energy of a body is changed, its mass (and weight) are
changed. The change in mass that accompanies a given change of energy is