The Concept of Energy 85
The conservation of energy is nothing more than the statement that
heat, motion and work are equivalent and that for a given amount of
work one gets the same amount of motion or the same amount of heat, or
that for a given amount of motion one gets the same amount of heat and
so on and so forth.
It requires energy in the form of work to give motion to a body, which
is initially at rest. The energy acquired by a body in motion is referred to
as its kinetic energy. Since all objects are composites of smaller particles
called atoms, which are also in motion, the motion of any object can be
separated into its external motion and its internal motion. The term, the
kinetic energy of a body, usually refers to the energy due to its external
motion. The energy of its internal motion, on the other hand, is by
definition heat. The amount of heat is exactly equal to the sum of the
kinetic energy of each atom’s internal motion. The amount of energy
required to move an object depends on its mass and the final velocity of
its motion. The greater either the mass or the velocity, the greater the
energy. Since energy was defined as a conserved quantity, the kinetic
energy of a body was defined equal to one half its mass times its velocity
squared (E = 1/2 mv^2 ) to insure that energy remains a conserved
quantity. Kinetic energy is not necessarily conserved as was illustrated
by bodies that slow down as a result of friction or the ball that came to
rest as a result of striking the Earth. In each of these examples the kinetic
energy is converted into other forms of energy such as heat in the case of
friction or in the case of a ball striking the Earth kinetic energy is
converted into heat, sound and a deformation of the ground.
As mentioned in our previous discussion of mechanics, a force is
necessary in order to change the velocity a body. In order to exert a force
however, energy must be provided in the form of work. The amount of
work done as a result of exerting a force is equal to the distance through
which the force acts, times the magnitude of the force in the direction
through which it acts. If a force acts perpendicular to the motion of a
body no work is necessary since this action will only change the
direction of the body and hence the kinetic energy will remain fixed. If
the body is pushed along its direction of motion, however, the speed of
the body will increase and hence the work being expended in pushing it
will be converted into the increase in the body’s kinetic energy.
Work can also be used to change the position of a body in a force
field by overcoming the force such as lifting a body from the ground to
some given height. The energy or the work done on the body is stored in