Page 96 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 7] ENERGY 81

RESTENERGY
According to Einstein’s theory of relativity, matter can be converted to energy and energy can be converted to
matter. The rest energy of a body is the energy it has by virtue of its mass alone. Thus, mass can be regarded as
a form of energy. The rest energy of a body is in addition to any KE or PE it might have.
If the mass of a body is m 0 when it is at rest, its rest energy is
Rest energy = E 0 = mc 2

In this formula c is the velocity of light in free space, whose value is
8
8
c = 3.00 × 10 m/s = 9.83 × 10 ft/s = 186,000 mi/s
2 8 2
This book has a mass of roughly 1 kg. The rest energy of a 1-kg object is E 0 = mc = (1 kg)(3×10 m/s) =
9 × 10 16 J, enough energy to send nearly a million tons to the moon. By contrast, the PE of this book on top
5
of Mt. Everest is less than 10 J. All the energy-producing reactions of physics and chemistry involve the
disappearance of a small amount of matter and its reappearance as energy.

SOLVED PROBLEM 7.22
9
Approximately 4 × 10 kg of matter is converted to energy in the sun each second. What is the power
output of the sun?
The energy produced by the sun per second is
8
2
26
2
9
E 0 = mc = (4 × 10 kg)(3 × 10 m/s) = 3.6 × 10 J
Hence the power output is
26
3.6 × 10 J
E 0 26
P = = = 3.6 × 10 W
t 1s
SOLVED PROBLEM 7.23
How much mass is converted to energy per day in a nuclear power plant operated at a level of 100 MW
6
(100 × 10 W)?
There are 60 × 60 × 24 = 86,400 s/day, so the energy liberated per day is
8
12
4
E 0 = Pt = (10 W)(8.64 × 10 s) = 8.64 × 10 J
2
Since E 0 = mc ,
12
E 0 8.64 × 10 J −5
m = = = 9.6 × 10 kg
8
c 2 (3 × 10 m/s) 2
CONSERVATION OF ENERGY

According to the law of conservation of energy, energy cannot be created or destroyed, although it can be
transformed from one kind to another. The total amount of energy in the universe is constant. A falling stone
provides a simple example: More and more of its initial potential energy turns to kinetic energy as its velocity
increases, until finally all its PE has become KE when it strikes the ground. The KE of the stone is then transferred
to the ground as work by the impact.
In general,

Work done on an object = change in object’s KE + change in object’s PE + work done by object
Work done by an object against friction becomes heat, as discussed in later chapters.