AN INTRODUCTION TO NEWTONIAN MECHANICS by Edward Kluk Dickinson State University, Dickinson ND

RECTILINEAR MOTION ON A HORIZONTAL PLANE

        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
d = v_o t ,
where v_o stands for an initial speed for each graph, t for elapsed time and d for covered distance. For each motion v_o can be found as a slope of its graph. Motions described by the discussed relation are called uniform motions because covered distances are increasing uniformly in time.

        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 v_o of each motion. If you are not sure about it use the formula for an average speed v_av which we have introduced in the former experiment v_av = ( d ₂ - d ₁ ) / (t ₂ - t ₁ ) .
Substituting d ₁ and d ₂ from the distance - time relation for uniform motion we obtain
v_av = v_o ( t ₂ - t ₁ ) / (t ₂ - t ₁ ) = v_o.
You should notice that starting with experimental dependence of covered distance on time and doing some elementary algebra, we have proven a constancy of speed for this motion.

        Evaluation
        If at this point you do understand:

• why ancient and medival scientists thought that in any circumstances to keep body in motion a force should be applied
• how the distane - time relation for uniform motion can be deduced from experimental data
• how the speed for a frictionless horizontal motion can be mathematically deduced from the distane - time relation
• what is difference between free fall and frictionless horizontal motion

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.