FORCED OSCILLATIONS

Galileo was not the only famous member of the Galilei family; his father Vincenzo was an accomplished and articulate musician.

WINDING UP THE MECHANICAL UNIVERSE

We've now arrived at the final chapter in our study of the mechanical universe. In our story we've introduced revolutionary ideas and heroes from Copernicus to Newton, and just as they did before us, we've linked the physics of the heavens to the physics of the earth.

THE AGE OF STEAM

The age of steam is past. The steam engine is a curiosity, an object of nostalgia that has been replaced by diesel engines, electric motors, turbine engines, and gasoline engines to drive the wheels of civilization. Nonetheless, steam did have its day. The steam engine not only caused the industrial revolution, which changed our lives, it also led to discoveries in physics so profound that they changed the way we think. How did investigations into the nature of steam engines lead to a deeper understanding of the universe?

First, we need to understand how a steam engine operates. In essence, a steam engine is a device which heats water in a dosed container, a boiler, thereby converting it to steam.

ANTIDIFFERENTIATION, THE REVERSE OF DIFFERENTIATION

We saw by examples in earlier chapters that laws of physics are often expressed as equations about the rate at which things change – that is, equations about derivatives.

In discussing falling bodies in Chapter 2, we started with a knowledge of the distance function (how far a body falls in a given time), then took its derivative to find its speed (how fast it is falling), and then took the derivative of the speed to find its acceleration (how fast it was getting faster).

FINDING THE CONNECTION BETWEEN ELECTRICITY AND MAGNETISM

The flood of forces identified and classified in the eighteenth century was reduced to a trickle after it was realized that electric forces were responsible for many phenomena. Nature, it seemed, acknowledged only a handful of forces. Each force had its own “universal constant.” For electric forces, it was Ke ; for gravity, G; for magnetism, there was an additional constant Km ; and for light, there was the speed of light, known since 1630 to be 3 × 108 m/s. Surely many physicists wondered whether these constants and the forces they represent are somehow related.

GENERAL INTRODUCTION

The Mechanical Universe is a project that encompasses fifty-two half-hour television programs, two textbooks in four volumes (including this one), teachers' manuals, specially edited videotapes for high school use, and much more. It seems safe to say that nothing quite like it has been attempted in physics (or any other subject) before. A few words about how all this came to be seem to be in order.

Caltech's dedication to the teaching of physics began fifty years ago with a popular introductory textbook written by Robert Millikan, Earnest Watson, and Duanc Roller. Millikan, whose exploits are celebrated in Chapter 12 of this book, was Caltech's founder, president, first Nobel prizewinner, and all-around patron saint. Earnest Watson was dean of the faculty, and both he and Duane Roller were distinguished teachers.

Twenty years ago, the introductory physics courses at Caltech were taught by Richard Feynman, who is not only a scientist of historic proportions, but also a dramatic and highly entertaining lecturer. Feynman's words were lovingly recorded, transcribed, and published in a series of three volumes that have become genuine and indispensable classics of the science literature.

The teaching of physics at Caltcch, like the teaching of science courses everywhere, is constantly undergoing transition. Caltech's latest effort to infuse new life in freshman physics was instituted by Professor David Goodstein and eventually led to the creation of The Mechanical Universe.

THE SEARCH FOR ORDER

In the sixteenth and seventeenth centuries, that brilliant awakening known as the Renaissance was brought to an end as Europe turned its attention to a spirited debate on the finer points of Christian theology. This period, known as the Reformation and Counter-Reformation, culminated in the bloody Thirty Years' War (1618–48).

At that time, three individuals devoted to physics and astronomy laid the foundations for the enormous scientific achievements of Isaac Newton.

THE COPERNICAN REVOLUTION

We find it difficult to imagine the frame of mind of people who once firmly believed the earth to be the immovable center of the universe, with all the heavenly bodies revolving harmoniously around it. It is ironic that this view, inherited from the Middle Ages and handed down by the Greeks, particularly Greek thought frozen in the writings of Plato and Aristotle, was one designed to illustrate our insignificance amid the grand scheme of the universe – even while we resided at its center.

Aristotle's world consisted of four fundamental elements – fire, air, water, and earth – and each element was inclined to seek its own natural place. Flame leapt through air, bubbles rose in water, rain fell from the heavens, and rocks fell to earth: the world was ordered.

TOWARD AN IDEA OF ENERGY

The law of conservation of energy is a fundamental law of physics. No matter what you do, energy is always conserved. The total amount of energy in the universe is, has been, and always will be the same as it is right now. So why do people tell us to conserve energy? Evidently the phrase conserve energy has one meaning to a scientist and quite a different meaning to other peopie, for example, to the president of a utility company or to a politician. What then, exactly, is energy?

THE DISCOVERY OF THE ELECTRON

In the 1890s physicists were puzzled by cathode rays, by glowing gases, and by applegreen fluorescence that appeared in their investigations of light. To study the light emitted by various elements, researchers had developed a specially designed glass apparatus called the cathode-ray tube. To two pieces of metal, called the cathode and anode, which pass through the tube, would be connected a powerful electric voltage as illustrated in Fig. 12.1. When the gas was at atmospheric pressure, nothing happened, but when the pressure was reduced to one-hundredth of atmospheric pressure, the gas began to glow. The end of the tube near the anode glowed, or fluoresced, with an eerie green color, except where a shadow of the anode appeared. Evidently, the cathode emitted mysterious rays – cathode rays – that streamed from the cathode to the anode. Some of these rays hit the glass, creating the green light, but others were blocked by the anode, creating a shadow.

THE END OF THE CONFUSION

In 1543, Copernicus published his book, and a tremor rocked the foundations of the Aristotelian worid. A century later the Aristotelian world lay in ruins, but nothing had arisen to replace it, Galileo and Kepler had made mighty discoveries, but there was no central principle that could organize the world. The unified harmony of the Aristotelian view had been replaced by buzzing confusion.

Galileo was concerned not with the causes of motion, but instead with its description. The branch of mechanics he reared is known as kinematics; it is a mathematically descriptive account of motion without concern for the causes.

NEWTON AND THE SPEED OF SOUND

At any given moment in the development of physics, there are certain experiments or measurements that are just barely possible. These are not the most difficult experiments we can imagine, but they are the most difficult experiments that one can effect with existing equipment. These experiments become a challenge to the artistry and imagination of the most gifted experimenters. A typical example today might be the detection of gravity waves. Toward the end of the seventeenth century, one such state-of-the-art experiment was to measure the speed of sound.

Sound is some sort of disturbance that most often travels to our ears through air. Sound also travels through liquids and solids, but in any case a medium, that is, a substance, is needed in order for the sound waves to travel. In a vacuum, there is no sound.

THE QUEST FOR PRECISION

Not long after Copernicus published his revolutionary book, Tycho Brahe (1546–1601) provided a multitude of new observations that, despite his own intentions, provided crucial support for the Copernican hypothesis.

CELESTIAL OMENS: COMETS

Ancient astronomers earned their keep and kept their heads by making accurate predictions of the arrival of the seasons and of such troubling ceiestiai events as solar and lunar eclipses. As their technical expertise improved, astronomers learned to predict even the wandering motion of the planets. Yet at times, interlopers, such as meteors, appeared in the night sky. Although meteors seemed as unpredictable as the weather (and were thought to be related to it, which is why their name shares the same Greek root with the science of weather – meteorology), even meteor showers were observed to occur regularly. For example, the most spectacular meteor showers occur every year in mid-August.

Nevertheless, objects occasionally and mysteriously appeared in the heavens which were not planets or meteors. Trailing plumes of cold fire, these objects were named comets, from the Greek word meaning thing with hair. Because their appearance was unpredictable, comets were interpreted as omens of impending disaster.