Newton's Laws

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**. **WHY objects move**, 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. Most particularly falling objects didn't behave exactly like the Greeks claimed. The Greeks had suggested that the elements of the 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,* requiring no further explanation, for objects to move up or down to where they belonged. So bubbles of

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 considering that the combined mass would be greater than either separately, so the combined objects would be required to 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 the Greek kinematics, he had no replacement for the Greek dynamics.**

**Isaac Newton** (b1642, d1727 ←portrait at left), who was born in a hamlet north of London on Christmas Day of the same year Galileo died, quietly and masterfully provided a replacement dynamics. Rather than attempt to PROVE Newton was right, we might first try to fathom the significance and implications of his proposal. Newton was a very solitary person who developed his own private understanding of the principles governing motion. In 1684 Newton's acquaintance, Edmund Halley, asked Newton's thoughts about the motion of planets. (**René Descartes** had proposed that planets' orbits are due to fluid vortices.→) Halley, finding Newton's mathematical and physical explanation superb, pushed Newton to further amplify his analysis. Halley arranged for the publication in 1687 of Newton's ** Philosophiae Naturalis Principia Mathematica.** This document is often regarded as the culmination of the Scientific Revolution, in which science as we know it today was born.

**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 were*Natural Motions.*So**henceforth such motions will need no further explanation of cause.**This idea was developed from earlier proposals by Galileo and Descartes.- 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. Substituting the definition of acceleration, the more general formula might later also be useful:**F = Δ(m v) / Δt**. **To every action there is always opposed an equal reaction**. The mutual actions of two bodies upon each other are always equal, and directed in contrary directions. 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 which had been previously meticulously studied and formulated by **Johannes 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.

Our modern world has provided us with a wealth of low friction toys and measuring devices such as accurate timer-watches and cameras capable of recording video sequences. The purpose is to **use whatever equipment is available to try to gather evidence that is consistent with Newton's laws.** (See Lab I-1 for hints about measurement tools and analysis.)

- 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.
- Find several lighter objects of know (labelled) mass (in grams), perhaps a box of labeled jello, or a small candy bar. This will be used to provide a known force.
- 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: m
_{1}x d_{1}= m_{2}x d_{2}. Solve the equation to find the mass of the toy. - Connect the toy with the known mass by a string passing over some object that allows the string to move with little friction.
- Let the known mass accelerate the toy, recording information to determine the acceleration.
- The easiest way to determine acceleration may be to use Galileo's formula: d = 1/2 at
^{2}. Solving for

we get**a****a = 2d / t**.^{2} - Repeatedly time the interval from release until the known mass hits the floor or other obstruction and find the average of
good

trials. - Measure the distance the front (or other fixed part) of the toy travels while being pulled by the known mass during the timed motion.
- Substitute the distance (from c) and the time (from b) into the equation (from a) to determine acceleration,
**a**. - Determine the force,
**F**, pulling the toy by multiplying the knownpulling 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! - 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.
- Substitute the Force (from e), acceleration (from d), and mass (from f) into
**F =**m**a**to determine if equal.

- The easiest way to determine acceleration may be to use Galileo's formula: d = 1/2 at
- Change the known force pulling on the toy to
**determine if acceleration is proportional to the force.** - Change the mass of the toy by attaching known masses to
**determine if acceleration is inversely proportional to the mass.** - Consider the possible extent of errors in masses, times, and distances, and the effects of possible errors on force, mass, and acceleration. In particular, consider if the possibility of timing error discussed in Experiment I-3, at the end of Part I applies.

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** technical report

,*Isaac Newton***Philosophiae Naturalis Principia Mathematica**, 1871 printing, Google Books. (also may download PDF version)

**to skill building exercises:**

Summary & Practice of Dynamics:

Vector analysis: describing motion in multiple dimensions

Force analysis: components, parallel forces

Analysis of projectiles, circular & harmonic motions

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latest revision 24 February 2013 by D Trapp