Physics: The Fundamental Science distance between Syene and Alexandria must be one-fiftieth of the earth's circumference During Eratosthenes time, the distance between these two cities was estimated to be 5000 stadia. So the circumfer- ence of the earth was 50 times this distance or 250 000 stadia. Although the exact length of that Greek unit is not known, we do know that the length of a Greek stadium varied between 154 and 215 meters. If we use an average value of 185 m, the result is only about 15% larger than modern measurements, a remarkable achievement. phenomena. It is a mystery to me,wrote the Nobel Prize inning physicist Sheldon Glashow, that the concepts of mathe- matics(things like the real and complex numbers, the calculus and group theory), which are purely inventions of the human imagination, turn out to be essential for the description of the real world Physicists, on the other hand, have invented powerful math ematical techniques in their search to understand the physical world. Newton developed the calculus to solve the problem of the attraction that the earth exerts on all objects on its surface Mathematicians later continued the development of calculus into what it is today. Mathematics is then the instrument of physics; the only lan- guage in which the nature of the world can be understood. None the less, in this book we are interested in the concepts of physics These concepts can usually be described with words and exam- ples. In some instances, however, there is no substitute for the elegance and conciseness of a simple formula. In these cases, re shall consider such a formula to see how it explains new con- cepts and how they can be linked to other concepts alread learned. The reader should always keep in mind that our purpose is to understand the physical phenomenon, not the mathematics that describes it
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2 THE DESCRIPTION OF MOTION Understanding motion The understanding of motion is fundamental in our comprehen sion of nature. To understand motion is to understand nature wrote Leonardo da Vinci. If we understand how an object moves we might be able to discover where it has been and predict where it will be some time in the future, provided that the present conditions are maintained. In physics, we are interested in the description of the motion of the different bodies that we observe, such as automobiles, airplanes, basketballs, sound waves, elec- trons,planets, and stars To study how objects move, we need to begin by studying how a simple object moves. An object without moving parts, such as a ball or a block, is simpler than one with separate parts because we do not need to worry about the motions of the parts, and we can concentrate on how the object moves as a whole. a ball can roll and a block can slide on a surface which one is simpler? It would be easier for us if we did not have to decide beforehand either the shape of the object or its internal structure. Physicists simplify the problem by considering the motion of a point, an ideal object with no size, and therefore no internal structure and no shape. We will consider first the motion of a point. However, in our illustrations and examples we might refer to the motion of real objects, like cars, baseballs, rockets or people. If we do not consider the internal structure of the object, and do not allow it to rotate, this object behaves like a point for our urposes
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SUPERSTRINGS AND OTHER THINGS Uniform motion My purpose is to set forth a very new science dealing with a very ancient subject, wrote Galileo in his Two New Sciences. He con- tinued:"There is, in nature, perhaps nothing older than motion, concerning which the books written by philosophers are neither few nor small; nevertheless I have discovered by experiment ome properties of it which are worth knowing and which have not hitherto been either observed or demonstrated Galileo, one of the first modern scientists and the first one to understand the nature of motion, was born in Pisa the same year that Shakespeare was born in England and three days before Michelangelo died The year was 1564. His full name was galileo Galilei, following a Tuscan custom of using a variation of the family name as the first name of the eldest son. His father. a renowned musician wanted his son to be a physician, a far more lucrative profession in those days. Thus, he entered the University of Pisa to study medicine. Upon hear- ing a lecture on geometry which encouraged him to study the work of Archimedes, the young medical student decided that science and mathematics seemed far more interesting than medicine. Galileo talked to his father about letting him switch Fortunately for the world his father consented Galileo became well known throughout Italy for his scientific ability and at the age of 26 was appointed Professor of Mathe- matics at the University of Pisa. There he dug deeply into funda- mental science. He also made some enemies, especially among the older and more respected professors, who did not like their opinions and views challenged by the young and tactless galileo Partly because of this, and partly because the Republic of Venice was, in 1600, the hub of the mediterranean which in turn was the center of the world, Galileo accepted a position as Professor of Mathematics at Padua, where he began the work in astronomy that was to bring him immortal fame Galileo's work on mechanics was published as Discourses and Mathematical Demonstrations Concerning Two New Sciences Pertain ing to Mechanics and Local Motion, which appeared in 1638. In the chapter"De Motu Locali"or"Change of Position", he writes The discussion is divided into three parts; the first part deals with motion which is steady or uniform; the second treats of motion a
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A Figure 2.1. Several positions of a runner running along a straight track. we find it accelerated in nature, the third deals with the so-called Galileo then goes on to explain what "motion which is steady or uniformis By steady or uniform motion, I mean one traversed by the moving particle during any equal interval of time, Figure 2.1 is an example of uniform motion; it shows several positions of an athlete running along a straight 100-m track at a steady pace. The marks alongside the track show that the runner moves equal distances of 10 meters in equal intervals of Average speed The runner in figure 2.1 travels 10 meters in six seconds or 100 meters in 60 seconds (1 minute). We can say that the runner travels at 100 meters per minute. Average speed is defined as the total distance traveled divided by the time taken to travel his distance. If we use the letter d to indicate distance, and the letter t to indicate time, we can write the average speed, i, as distance traveled d time taken
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SUPERSTRINGS AND OTHER THINGS Figure 2.2. Multiple-exposure photograph of a disk of"dry ice"moving on a smooth surface. (lllustration from PROJECT PHYSICS, copyright C 1981 by Holt, Rinehart and Winston, Inc. Reprinted by permission of the where the bar above the letter v is used to indicate that this is the average value. The runner of our example travels a distance of 100 meters in one minute. The average speed of the runner, 100 m /min Figure 2.2 shows a multiple-exposure photograph of a disk of solid carbon dioxide(dry ice)in uniform motion. The disk, resting on the polished surface of a table, is given a gentle push With the room darkened, the shutter of a camera set on a tripod is kept open while at equal intervals of time a strobe is fired. Since the only source of light comes from the strobe which for this experiment was fired at 0.10 second intervals the film records the position of the disk as it slides on the table The meter rule shows that the disk moves 13 cm between flashes The disk, then, traverses equal distances of 13 cm in equal inter- vals of 0.10s or 130 centimeters in 1.0 second. We can say that the disk travels at an average speed 0=130 centimeters per The units of speed are units of distance divided by units of time. Speed can thus be given in miles per hour, kilometers per hour, meters per second, feet per minute, etc. The SI unit of speed is the meter per second(m/s) In both of those cases, the speed did not change. The runner and the disk were moving at a uniform or constant speed, at least for the intervals that were considered However few motions are uniform. The most common situation is that of variable speed. If you drive from your dorm to the movies, you start from rest, speed up to 30 miles per hour and probably drive at that speed 28
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