ie-Physics

Experiment I-4

The ancient Greeks not only tried to describe the world, but they also tried to explain why the cosmos behaves as it does.  The study of HOW objects move came to be know by the term kinematics.  The WHYs of motion, so capably explained by Aristotle, became known as dynamics.

Like most human efforts, the Greek explanations were not perfect.  Over the centuries a few weaknesses were found.  Several noteworthy Arabs proposed improvements.  By 1630, nearly 20 centuries after Aristotle's original efforts, most educated people in the western hemisphere still found the his Greek explanations substantially matched the observed world.  Aristotle's explanations still seemed reasonable.

One of the weakest Greek explanations was that of motion.  Things that change, and most particularly falling objects, didn't behave exactly like the Greeks claimed.  The Greeks had suggested that the elements of world, earth, water, air, and fire, all have their natural place.  Earth, being the heaviest, belongs at the center of the earth which was also the center of the universe.  It was natural and required no further explanation for objects to move up or down to where they belonged.  So bubbles of air float upward in water as does wood which contains more air than earthy ashes.  This, plus the other natural motions of living things and heavenly bodies caused all other changes.  That all seemed reasonable.  But projectiles posed considerable difficulties.  A living person could throw a projectile, but why did it keep going and not immediately fall upon its release?  Many agreed with the Arab proposal that a projectile might contain something called impetus that would carry it a ways, but once consumed, would allow the projectile to belatedly fall.  Galileo Galilei in his Discourses and Mathematical Demonstrations Concerning Two New Sciences (1638) attacked this weakness and argued that Aristotle's explanation of falling could not be correct.

For example Galileo considered the fall of two objects of different weights tied together.  Aristotle said the heavier fell faster.  Tied together, the heavier would tug on the lighter making it faster, and the lighter would retard the heavier, so that together they would have an intermediate speed.  But the combined mass would be greater than either separately, thus requiring a fall even faster than the heavier alone.  So Aristotle's explanation was internally contradictory.  The objects tied together couldn't have both kinematics!  So Aristotle's dynamics could not possibly be correct.  While Galileo attacked and overthrew the Greek kinematics, he had no replacement for the Greek dynamics.

Isaac Newton (b1642, d1727 ←portrait at left), born Christmas Day in the year of Galileo's death, quietly and masterfully provided a replacement dynamics.  It is not for us here to now PROVE Newton was right.  Rather it is for us to try to fathom the significance and implications of what he proposed.  Newton was a very solitary person who developed his own private understanding, then had to be convinced by his acquaintance, Edmund Halley, to write it down for their colleagues' benefits.  Halley arranged for the publication of Philosophiae Naturalis Principia Mathematica in 1687.  This document is often regarded as the culmination of the Scientific Revolution, in which science as we know it today was born.

1. Every material body persists in its state of rest or of uniform motion in a straight line if and only if it is not acted upon by a net external force.  In this simple statement, Newton replaces what for Aristotle was Natural Motion and henceforth will need no further explanation.  This idea was developed from claims by Galileo and Descartes.
   
   
2. An object upon which an unbalance force is exerted will be accelerated proportional to that force and in the direction of that force, and inversely proportion to the object's mass.  This relationship, often summarized by the equation F = ma, is one of the most powerful relationships ever proposed.
   
   
3. To every action there is always opposed an equal reaction.  The mutual actions of two bodies upon each other are always equal, and directed to contrary parts.  For every force UPON an object, there is an equal opposing force BY that object.  Newton originated this brilliant insight.  With it he provided a crucial way to understand many situations where forces are otherwise undeterminable.

Finally, Newton uses these rules to demonstrate that they account for the motions of the earth, planets, and moons that had been meticulously studied and formulated by Kepler.  Newton's laws, coupled with his Law of Universal Gravity and similar laws for other forces, could adequately explain all motions whether here on earth or in the heavens.

Experiment

Our modern world has provided us with a wealth of low friction toys and measuring devices such as accurate timer-watches and video cameras.  The purpose is to use whatever equipment is available to try to gather evidence that is consistent with Newton's laws.

1. Find a toy that moves with little resistance.  Check this by rolling along a smooth counter top to determine if it coasts at nearly constant speed as would be expected by Newton's first law.
2. Find several lighter objects of know mass (in grams), perhaps a box of labeled jello, or a small candy bar.  This will be used to provide a known force.
3. If you don't have a balance to find the mass of the toy, use a ruler for a make-shift balance.  Hold the ruler by a string through its middle, hang an object of know mass from one end of the ruler, and find the location for hanging the toy that just balances the known mass.  The product of the know mass times its distance to the middle must equal the mass of the toy and its distance to the middle: m₁ x d₁ = m₂ x d₂.  Solve the equation to find the mass of the toy.
4. Connect the toy with the known mass by a string passing over some object that allows the string to move with little friction.
5. Let the known mass accelerate the toy, recording information to determine the acceleration.
   1. The easiest way to determine acceleration may be to use Galileo's formula: d = 1/2 at².  Solving for a we get a = 2d / t².
   2. Repeated time the interval from release until the known mass hits the floor or other obstruction and find the average of good trials.
      
   3. Measure the distance the front (or other fixed part) of the toy travels while being pulled by the known mass.
   4. Substitute the distance (from c) and the time (from b) into the equation (from a) to determine acceleration, a.
   5. Determine the force, F, pulling the toy by multiplying the known mass by the acceleration due to gravity (found in Experiment I-3).  Note that Newton's Third Law says the pull of gravity on the known mass is equal and opposite the pull of that mass on the Earth!
   6. Note that both the toy and the pulling mass are tied together and both move as if there were one body due to the weight of just the known mass.  So add the mass of the toy and the pulling mass, m.
   7. Substitute the Force (from e), acceleration (from d), and mass (from f) into F = ma to determine if equal.
6. Change the known force pulling on the toy to determine if acceleration is proportional to the force.
7. Change the mass of the toy by attaching known masses to determine if acceleration is inversely proportional to the mass.
8. Consider the possible extent of errors in masses, times, and distances, and the effects of possible errors on force, mass, and acceleration.

Finally, record your procedures, measurements, and findings in your journal.  If you need course credit, use your observations recorded in your journal to construct a formal report

Reference

• Isaac Newton, Philosophiae Naturalis Principia Mathematica, online editions by Burndy Library, 1687, 1713, 1726. (Caution, each edition is large and will require significant download time.)