Northern Illinois University
Physics 150
Lab 5 Recitation Notes
Conservation
Mechanical energy exists in one of two forms, either potential energy or kinetic energy.
Potential energy is stored energy or the energy an object has because of its position. Examples of
objects possessing potential energy include a compressed spring or a book sitting on a desktop.
In the case of the spring, it may be released to do work, much as you might see at an arcade
when the "launch" rod of a pinball machine is released and the pinball is shot into the field of
play. If the book is allowed to fall to the floor, its potential energy will be converted to sound
(the "thud" as it hits the floor) and heat, admittedly a small value.
On the other hand, kinetic energy may be considered to be the energy of motion. A speeding car
has kinetic energy. A fired bullet has kinetic energy. Less obvious, but no less valid is the kinetic
energy that a glacier has. It has a velocity that may only be a fraction of an inch over the period
of a year, but it is moving and hence, does have kinetic energy.
An object may have both kinetic and potential energy. Consider a passenger airplane in flight. At
a velocity in excess of 500 miles per hour, it has obvious kinetic energy. Equally obvious is the
potential energy it has as a result of its altitude.
The total amount of energy in the universe is taken to be constant, inferring that energy can
neither be created nor destroyed. However, energy is routinely converted from one form to
another. In fact, one widely held definition of physics is that is merely the study of such energy
conversions. Examples include the evaporation of seawater, which is conversion of the sun's
radiant energy to the potential energy of elevated water vapor. When the vapor condenses and
rains results, the potential energy is converted to kinetic energy. If enough rainwater is collected,
damned, and then directed over water wheels, it may be used to generate electricity, another
conversion. You should see that when there is talk of an energy shortage, this is not an accurate
statement. If the amount of energy available today is the same as it was millions of years ago,
how could there be a shortage? Rather, it would be more accurate to say that our capacity to
convert available energy to usable energy is limited or changing.
The kinetic energy of an object may be calculated by
KE = 1/2 mv2 where m  mass of the object in kg
v velocity of the object in m/s
The unit of kinetic energy is the joule J, equal to a kg m2/s2 or N m.
In order to impart an object with kinetic energy (to get it moving), it is necessary to apply a net
accelerating force over a discrete time, according to Newton's second law:
F = ma where a  acceleration
Having accelerated a massive object ("massive" indicating that the object has mass) to a nonzero velocity imparts the object with momentum according the equation:
p = mv where p  momentum in kg m/s
Until a net force is applied to the object (friction, air resistance, etc) the object cannot be
accelerated. In the absence of acceleration, its velocity will not change. If its velocity remains
constant, its momentum will not change. The same logic holds true for a group of objects.
Consider the case of a spring compressed between two cars. Together, the spring and the cars
comprise a group of objects, commonly referred to as a system. If the cars are at rest (v = 0), their
momentum must also be zero. When the spring is released, the cars are propelled away from one
another in opposite directions. It is obvious that each car individually has momentum since each
has a velocity. What may not be so obvious is that the momentum of the system is still zero. No
net external force has been applied. Hence, by definition, momentum remains unchanged.
Recalling that our description of velocity must necessarily include direction, you should be able
to conclude that the opposite directions of travel of the cars accounts for opposite signs of
momentum that cancel, preserving the system momentum at zero.
Now consider the case of two cars that collide. If no outside forces are applied, momentum must
remain unchanged. In physics, "unchanged" quantities are said to be "conserved". In this case, as
with the cars that push away from one another, momentum is conserved. Total energy is also
conserved. Conversion of energy from one form to another may make it more difficult to accept
conservation.
There are two types of collisions. An elastic collision is defined as one in which kinetic energy
of the system is conserved. Alternatively, an inelastic collision is characterized by kinetic energy
loss as might be expected in an automobile accident. Perfectly inelastic collisions occur when
the objects involved actually stick together, moving as one unit afterward.