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AN INTRODUCTION TO NEWTONIAN MECHANICS by Edward Kluk Dickinson State University, Dickinson ND |
A
historical overview
A single push of an object resting on
a rigid horizontal plane makes this object moving along a
straight line. But after a while the object will stop. This
simple observation is known for human beings for many thousands
years. In 4th century BC Greek philosopher and scientist
Aristotle postulated that keeping a body in motion
with a constant speed demands a constant push. Or we may say,
application of a constant force. But we have to admitt a
vagueness of idea of force in this kind of statement. It does not
tell us how to measure a force, then it does not have practically
any scientific value. It took two thousands years and Isaac Newton
to refine Aristotle's postulate and create fundamental theory of
motion. Here we will make a first step in this direction.
Actually it is not difficult to
perform a following experiment. Take a hockey puck, set it flat
on a well leveled big sheet of sand paper and give it a
single slight push. The puck will not move very far. Replace the
sand paper by concrete surface, a board covered with formica, and
finally a smooth ice surface. It is clear that the same push will
make the puck to travel longer distance as we are changing the
surfaces. Probably everybody would say that such results are
obvious because in each consecutive case we deal with less
friction. A point here is to imagine yourself what would happen
if there were no friction at all. Well, it looks like the puck
should move with a constant speed across such frictionless
surface. Then Aristotle was not quite right because if there
is no friction, no force is needed to keep a body in motion.
The last paragraph presents an
example of abstraction method applied in science. Without having
possibility to experiment with a frictionless motion we were able
to deduce that keeping body in motion does not require any force,
unless a friction, or possibly other forces trying to stop the
body are present. Therefore bodies by their nature are trying
to preserve (conserve) a status of their motion.
Understanding how the simple experiments with hockey puck lead to
such conclusion is very important as an introduction to Newton's
laws of motion. Predesessors of Newton were not able to realize
that if a force is needed to keep a body in motion this force is
used only to overcome friction forces trying to stop the body.
An "experiment" on
frictionless surface and data analysis
This experiment is designed to help
you understand relations between an abstract frictionless motion
and its mathematical model (description). Select an initial
speed, start the motion and collect data representing covered
distance versus time. To do so, you have to start the motion with
selected initial speed several times. Remember, you cannot stop
this motion. When it stops, reset it to its original position and
start again. You may collect data for two or three different
initial speeds.
Now graph your data and convince
yourself that the results can be described with help of the
relation
Math helps to reach more
conclusions
Math wizards can see right away from
the distance - time relation that speeds for investigated motions
are constant and equal to vo of each
motion. If you are not sure about it use the formula for an
average speed vav which we have
introduced in the former experiment
Evaluation
If at this point you do understand:
the objectives of this lesson are fully achieved. If you have doubts try to read it once more concentrating on them, but do not try to memorize this text. physics is not about memorizing, it is about understanding.
| Last update: Jan 10, 1997 | E - mail to Edward Kluk |
| Copyright (c) 1996 Edward Kluk | |