Reasons Why the Measurement of Physical Quantity is Always ...



PHYS 210 (Physics I)PRIVATE (Classical or Newtonian Mechanics)IntroductionPhysics is a fundamental science subsuming subjects ranging from atoms and the subatomic particles of which atoms are made to galaxies and their constituents - pulsars, black holes, neutron stars, white dwarfs, and even the sun and our own earth. Physicists search for general laws that bring understanding to the chaotic behavior of our surroundings. The laws discovered, often seem obvious, yet their discovery usually requires years of theorizing and experimentation.For example, Apollonius of Perga, Pamphylia (now Turkey) in 200 B.C., adopted the concept that the earth occupied the center of the revolving Universe. Three hundred years later Ptolemy provided a theory to explain the complicated motion of the planets in the Earth-centered universe. Ptolemy's theory, which predicted with surprising accuracy the changing positions of the planets, was accepted for the next fourteen hundred years. Then Copernicus, who studied astronomy at the time Columbus sailed to America, developed a theory of motion for the heavenly bodies; the Sun resided at the center of the Universe and the Earth moved in orbit about it just as did the other planets. More than a hundred years later, the theory was confirmed by careful observation by Galileo Galilei. Finally, fifty years after Galileo's death, Isaac Newton formulated three simple laws of motion and the Universal Law of Gravitation, which together provided the basic understanding needed to explain the orbital motion of the earth and other planets.The simple laws developed by Newton give us the understanding needed to guide rockets to the moon, to build skyscrapers, and to realize why we should not lift heavy weights when in bent position. Newton's inspiration provided not only the basic resolution of the eighteen-hundred-year-old problem but also a general framework for analyzing the mechanical properties of nature. Now, three hundred years after Newton's death, we are able to learn these basic laws of motion and to use them during the first few weeks of physics course. It is hard to appreciate the great struggle of our predecessors who developed the understanding that now seems routine.At present, those same struggles occur in most branches of science with only the subject matter changing. How does the brain work? What causes the earth's magnetic field? What is the nature of the pulsating sources of x-ray radiation in our galaxy? Are protons and neutrons really made of three smaller particles called quarks held together by exchanging other particles called gluons - or is this quark theory a misconception such as Ptolemy's complicated model of an earth-centered universe?The pursuit of basic understanding often seems greatly moved from the activities of daily living. How could knowing that a proton is made of three smaller particles called quarks possibly affect our lives? Contemporaries of Joseph John Thomson could just as easily have asked him a similar question in 1897 after his discovery of the electron. He probably could not have provided a satisfactory answer. Yet, less than a century later, the electron plays an integral part in our lives. Moving electrons in electric circuits produce light for reading; heat for cooking; waves for transmitting news, stock quotations, and information about bank accounts; and much of the info provided by radio, television, and high-fidelity systems. Could quarks, if discovered, possibly bring such a technological revolution in the one hundred years following their discovery? The answer is almost certainly yes, but the revolution cannot be envisioned now, just as Thomson could not envision the technology initiated by his discovery.In the succeeding lessons the focus is on developing an understanding of the important, basic laws of physics. The said laws encompass subjects as mechanics, energy, waves, light, optics, electricity, magnetism, and the modern topics of atoms and nuclei. Just as important, we will try to foster the ability to use these laws to analyze relevant problems of current interest in physics and other fields of science and technology such as biology, medicine, geology, architecture, engineering, agriculture, and anthropology. If time permits, you would also learn about techniques used archeologist to determine the age of bones, about electron microscopes, airport metal detectors, ways in which heat is gained and lost in homes, the development of stresses and tensions in body muscles, and a variety of other subjects. Thus, you will see how the intellectual struggles of scientists in the past have led to relevant endeavors and that they provided part of the basis for your own future explorations of our interesting world.Science Defined.Science is a process of seeking and applying knowledge about our universe. It can be divided/classified/categorized into physical, life, and social sciences. Science (from Latin, scientia, meaning “knowledge”) is a systematic enterprise of gathering knowledge about the world and organizing and condensing that knowledge into testable laws and theories.Physics Defined. Physics is a science that deals with matter and energy and their interactions in the fields of mechanics, heat, electricity and magnetism, optics, acoustics, atomic structure and nuclear phenomena. Or, the study of the laws that determine the structure of the universe with reference to the matter and energy of which it consists. It is also defined as the study of physical forces and qualities: the scientific study of matter, energy, force, and motion, and the way they relate to each other. Physics traditionally incorporates mechanics, electromagnetism, optics, and thermodynamics and now includes modern disciplines such as quantum mechanics, relativity, and nuclear physics.Major Fields in Physics1.Mechanics (classical or Newtonian). A branch of physical science that deals with energy and forces and their effect or relation to the equilibrium, deformation, or motion of solid, liquid, and gaseous bodies. This branch of physics deals with motion of bodies, the concept of force, the effect of forces on motion and the form or shape of bodies, energy, momentum, work, and power. Properties of solids, liquids, and gases are likewise studied in this branch.a.Statics. A branch of mechanics which broadly concerns with the action of forces when no change of momentum (a measure of the difficulty encountered in bringing an object to rest) is concerned. Or, a branch of science that deals with bodies at rest or forces in equilibrium - forces acting on objects that are either at rest or moving at constant speed in a straight path. b. Dynamics (Kinetics). A branch of physical science and a subdivision of mechanics that is concerned with the motion of material objects in relation to the physical facts that affect them: force, mass, momentum, energy. Or, a branch of mechanics concerned with motion of bodies under the action of forces.c. Kinematics. A branch of mechanics studying the description of motion of bodies without reference to the forces causing the motion.d.Fluid Mechanics. A science of the interaction between forces and fluids. Or a branch of mechanics that deals with the special properties of liquids and gases.2.Acoustics. The study of sound and sound waves. Its study leads to the consideration of waves and wave motion. This also deals with the different sources of sound, its transmission through various media, acoustics, and hearing.3.Heat. This branch of physics deals with the temperature scales and measurement, the concept of heat, thermal expansion, heat capacities of substances, changes of state, heat transfer, and thermodynamics which is concerned mainly with the relationship between work and heat.4.Electricity. This branch of physics focuses on the concepts of electrical changes, the flow of electrical charges - better known as current, the various effects of current, electrical instruments, electrical and magnetic properties of matter, and electronics.5.Optics. This branch is concerned with the fundamental concepts of electromagnetic waves, absorption and transmission of light, reflection, refraction, optical instruments, and other various phenomena, such as, interference, diffraction and polarization. Or, the branch of physics that deals with vision and the properties of light.a.Geometrical optics assumes that light travels in straight lines and is concerned with the laws of controlling the reflection and refraction of rays of light.b.Physical optics deals with phenomena that depend on the wave nature of light, e.g. diffraction, interference, and polarization.6.Atomic & Nuclear Physics. This branch deals with the study of radiation, photoelectric effect, x-rays, structure of the atom, radioactivity, nuclear disintegration, and other properties of nuclei.Review Test1.Who said that the earth occupied the center of the revolving universe? ______________________________2.Who theorized the complicated motion of the planets in the earth-centered universe?_____________________________3.Who provided us the basic understanding needed to explain the orbital motion of the earth and other planets.____________________________4.Who discovered the presence of electron? _______________________________Who developed the theory of motion for the heavenly bodies and that the sun resided at the center of the universe, which was confirmed more than a hundred years later by Galileo Galilei? _____________________________ Measurements and Units Objectives:1.Distinguish fundamental quantities and units from derived quantities and units2.State the importance of measurement in the development of physics.3.Convert from one system of measure to another and convert units from smaller to bigger measures or contrariwise in the same system using a conversion factor.4.Identify Significant Figures (digits) and rounding off of numbers.5.Express numbers in standard form in terms of the powers of ten, prefixes, or scientific notation.6.Develop skills in solving problems by the use of scientific method, logical reasoning and reflective thinking.7.Develop manipulative skills in the use of precision measuring instruments.INFLUENCE, SCOPE AND FIELD OF PHYSICSPeople of early times were filled with fear and superstition because of ignorance and lack of understanding of the natural causes of happenings such as storms, floods, diseases, and death. It is man's knowledge in physics (the science that deals with the phenomena of life) that helps him understand his environment and the causes of change.They believed that things happened because of the powers of certain god and goddesses, faith in customs, sayings, and good luck and bad luck. And it is unfortunate, nowadays (this modern time), there are still people, mainly those living in the remote or rural areas, still have the same beliefs. Is it mainly because of their lack of education, particularly in the field of physics? I guess not. As a matter of fact, even educated people do adhere to a lot of superstitions. Perhaps, it would be easier to educate people living in the tribal or rural areas than educated people living in urban areas.Despite of man's ignorance during those dark times, there were a few who were deep thinkers, and these were commonly known as philosophers - people who attempt to seek answers to all forms of problems with arguments and discussions. Later, Aristotle, one of the Greek philosophers, influenced people through his teachings that proof was a necessity before a conclusion was made. He was interested in science and made several notable conclusions, such as "heavy objects always drop faster than a light one"; that "light is propagated through a transparent medium." Both conclusions, which were believed to be true for many years, however, were proven false a long time ago.Travel has been broadening man's horizon and has been leading him to think more intelligently. It has been discovered that many statements of philosophers needed and still need to be modified, if not totally changed. Galileo Galilei, one of the great thinkers, proved that heavy objects do not fall faster than light objects by his experiment performed at the famous leaning tower of Pisa. This experiment attracted wide attention and opened the way to more scientific investigations, which caused the rapid changes in our material world.Today, we live in the era known as the Computer Age. Conveniences in life and often life itself seem to rest upon the furtherance and practical outcome of science and technology. Of course, to a believer, our life itself absolutely rests upon God. Science today has profoundly influenced our way of life and it has given us confidence in our supremacy.Physics is observation - a process of gathering facts. It should be noted, however, that a mere collection of facts does not constitute science. Correlation and analysis of gathered facts must immediately follow. Two seemingly different phenomena may turn out, after careful analysis, to be related to each other. After correlation of facts, a theory based on these facts can be made. In essence, this is trying to predict some phenomena based on previously gathered and analyzed information. Finally, an experimental verification is attempted to see if the theory is correct. If the experimental result does not come out as predicted by the theory, the theory may be modified or augmented until it agrees with the experimental results. If, after so many experiments, the theory always predicts the outcome correctly, then the theory may be said to be correct and may lead to the formulation of law - a law of nature.The language of physics must be accurate and rigorous. Anything that is described and explained in physics must be carefully worded. Definitions of terms used in physics must be examined in detail, and the learner will save himself plenty of trouble if the definitions are well understood. Anyone who tries to memorize without understanding will most likely run into difficulty. Very often, the language of physics is translated into mathematical symbols and equations. This only implies the exactness imposed in the study of physics. The mathematical symbols and equations should be examined and scrutinized as closely as possible and the student must always attempt to translate it back into words with definite physical meaning. A working knowledge of algebra, trigonometry, and geometry is significant.MEASUREMENT. A figure expressing extent and/or property. Or, the determination of the magnitude, amount, or other parameter of a characteristic or quantity. Measurand is the physical quantity, property, or condition that is to be measured. Measuring is important for observing and doing research. It tells how far, how large, and how much. When you measure, you compare a known amount, called a standard, to an unknown amount. When you measure the length of lumber in meters, you are comparing the lumber’s length with that of a meter stick.To compare quantities, we have to specify two things – a number and the unit of measurement (e.g., 7 meters, 10 pounds, 30 seconds).Reasons Why the Measurement of Physical Quantity is Always Subject to Some Degree of UncertaintyThe limitations inherent in the construction of the measurement instrument.The conditions under which the measurement is made.The different ways in which the person uses or reads the measuring instrument.The Uncertainty of a Measurement can be Expressed in Terms of Accuracy and PrecisionAccuracy is the closeness of a measurement to the accepted value for a specific physical quantity. It is expressed as either an absolute or a relative error. Absolute Error is the actual difference between the measured value and the accepted value. Ae= Vm-Va Relative Error is often called percentage error.Re= AeVa x 100%Where:Ae = Absolute errorVm = Observed or measured valueVa = Accepted valueRe = Relative errorPrecision is the agreement among several measurements that have been made in the same way. It tells how reproducible the measurements are and is expressed in terms of deviation.Absolute Deviation is the difference between a single measured value and the average of several measurements made in the same way.Ad= Vm-Var Relative Deviation is the percentage average deviation of a set of measurements.Rd= Ad (average)Var x 100%Where:Ad = Absolute DeviationVm = Observed or measured valueVar= Mean or average of several readingsRd = Relative DeviationSystem of MeasurementThe development of science was delayed so much by two great handicaps - the cumbersome number system and the systems of measurements and computations. Prior to the 13th century, Roman numerals were used. To write a number in the said system is difficult; much more, if you try to add, subtract, multiply or divide Roman numbers. Besides, it has no symbol for zero.The Arabic system finally replaced the Roman, Babylonian and other number systems in the 16th century when measurement was used as a device to learn about reality or truth of nature. It was during this period that men performed both qualitative and quantitative experiments when observing the phenomena of life. They asked, "How does it happen?" and "How long will it happen." By then, man realized the vital role that measurement plays in our life as we use it everything we do.Without the development of the new number system and standard systems of measurement, the science of physics would not have been so precise as it is today.** In dealing with physical quantities, the question "how long?" or "how much?" is usually asked and this leads to the process of measurement. Measuring anything is simply a comparison with some given standard.Methods of Measurement.1.Direct Method. A method in which the measuring tool is directly used to determine the measurement of a certain quantity (usually with no computation needed). For example, if the length of one edge of the table is to be measured, a stick or a rod of a certain length is placed on the said edge of the table and the number of times or a fraction of the stick that will cover the whole edge of the table is determined. The length of the table is then said to be a fraction or so many times that of the length of the stick. This is clearly a case of comparison between the length of the stick and the length of the table with the length of the stick as the standard of comparison.2.Indirect Method. A method in which the measurement of a certain quantity is determined with the aid of equation and dependent on one or more quantities which have to be directly measured yet, or which may have been measured already. For example, the area of a rectangular table is to be measured, the length of two edges of the said table may be determined and the area can then be computed. Note that the area itself is not compared with a standard area but instead, a computation was made from the two quantities needed to be directly measured - the length and the width of the table. If the area of a round table is desired, the radius or diameter can be determined and with the given equation, the area of the table can be computed. The radius or diameter is directly measured and the area is indirectly measured.There are many physical quantities to be dealt with in physics -length, area, volume, speed, acceleration, power, energy, electric current, viscosity, and pressure, to name a few. Fortunately, and rather surprisingly, they can be reduced to and/or derived from the three fundamental quantities - length, mass, and time.In physics and in some other branches of science, the quantities used to describe nature are defined so that they have the same meaning for any person using them. Each quantity, when measured, has a magnitude (a number) and unit of measure.An essential component of measurement is precise standards that define units such as the meter. Standards have not always been defined precisely. At time a "foot" was the length of the king's foot in England. Property evaluations in Brooklyn were made using the U.S. foot, the Bushwick foot, the Williamsburg foot, and the foot of the 26th ward. Some strips of Brooklyn property were untaxable because after surveys made using different"feet," these strips of land legally did not exist!Perhaps, it is now clear that it is important to have standards that are precisely defined and that are used in common by people involved in trade, science, and industry.Systems of Units (consists of a set of standards for some or all basic units).1.SI System (international system of units). The modernized version of the metric system, based on atomic standards. Today, SI Units are used in most world trade and science and otherwise known as MKS and/or cgs system. One big advantage of this SI system is that large and small units are all related to the basic units by powers of ten. For example, 1 kilometer = 1000 meters, and 1 centimeter = 1/100 meter. Obviously, it is much easier to convert meters to kilometers than to convert feet to miles.Basic Units of the SI System--------------------------------------------------------------------------------------------- QuantityUnit NameUnit Symbol---------------------------------------------------------------------------------------------LengthmetermMasskilogramkgTimesecondsElectric CurrentampereATemperaturedegree kelvinKAmount of SubstancemolemolLuminous Intensitycandelacd---------------------------------------------------------------------------------------------2.English System. The system that evolved from English-speaking countries, and uses foot for length, pound for mass, and second for time. It is otherwise known as thee fps (foot-pound-second) system.In our country, the Philippines, both systems still prevail, so that one has to make a troublesome conversion process from system to another.fundamental units. Units assigned to fundamental quantities - meter, foot, gram, pound, second, and hours.derived quantities. All other quantities that can be derived from a combination (product(s) and/or quotient(s)) of one, two, or all of the fundamental quantities.derived units. Units assigned to derived quantities - square meter, cubic inches, miles per hour, pounds per square inch, and gram centimeter per second.the choice of units is purely by convention.Standard LengthMeter. Originally defined as the distance between two lines inscribed on a bar of metal stored in a special vault in a small town near Paris, France. A metal bar such as used for the length can deteriorate with time and is accessible to only a few. Therefore, it was redefined in 1960 in terms of the wavelength of light emitted by a particular atomic transition. It was further, redefined, however, in 1983 as the distance traveled by light in a vacuum in the time interval of 1/299,792,458 second. This latest redefinition equals the length of the old but is more accurate than the old, is accessible to scientists in any laboratory in the world, and does not deteriorate.Yard. This unit of length is commonly used by English-speaking countries. There is also a prototype or model for the yard which is kept in the Office of Exchequer in London, England. In the U.S., by an act of Congress, one yard is defined in terms of the meter by the relation, 1 yard = 3600/3937 meter. One-third of the yard is called the foot and one inch is equal to 1/12 of a foot (1 yard = 3 feet, 1 foot = 12 inches)Standard MassKilogram. A mass of block equal to that of international platinum-iridium prototype kept by the International Bureau of Weights and Measures at Sevres, near Paris. Originally, it was intended that the kilogram be equal to 1000 times the mass of a 1 cubic centimeter of water @ 4C, but there is a slight difference from this original intention and that of the standard kilogram. The difference, however, is rather small that it can be neglected for many purposes.Pound. The unit of mass in the fps system of units defined as 0.45359237 kilogram (1 kg = 2.204622622 lbs).Standard TimeThe unit of time commonly used is based on the time interval for the earth to make one complete rotation about its own axis. This time interval is called solar day and is the time it takes for the sun to make two successive passages across a meridian. Mainly because of the elliptical orbit of the earth around the sun, the solar day varies somewhat from one day to another. Thus a solar day during a summer month is longer than a solar day, say, during the month of November. The mean solar day is the average interval of these different solar days for one whole year. One second is defined as 1/86400 of the mean solar day (1 mean solar day = 24 hours; 1 hour = 60 minutes; 1 minute = 60 seconds).* Rotation of the earth about its own axis is used as a measure of time. Other types of repeated motion are used as devices for measuring time (e.g., the oscillation or swinging of a pendulum and the oscillation of a balance wheel, which the ordinary wrist watches has). A type of watch was developed which depends on the vibration of a tiny tuning fork. Note that all devices for measuring time make use of a repeated or periodic motion. A unit for the second has been adopted where the vibration of cesium atoms is used as the standard, that is, 1 second = 9,192,631.770 cesium vibrations.Dimensional Analysis. The study and analysis of the dimensions of the derived quantities. Or, a method of checking an equation or a solution to a problem by analyzing the dimensions in which it is expressed. (Dimension – a measurement of something in one or more directions, such length, width, or height) Dimensions are basic types of units, such as time, length, and mass.In any equation in physics, the dimension of the left side of the equation must always be the same as that of the right side. In addition, no two terms can be added or subtracted unless they have the same dimension. It is very instructive to check these dimensions to verify the validity of the equation being used. Habitual check on these dimensions is strongly recommended; the learner will gain more insight on the quantities he is dealing with whenever a dimension analysis is made.Example:s = v tWhere s = distance with the dimension Lv = velocity with the dimension L/T t = time with the dimension TL = LTT; L = LSometimes, it is more convenient to use power of ten prefixes when dealing with very large and very small numbers than using numbers with a lot of zeroes before or after the decimal points. (Refer the table that follows)Power of Ten Prefixes----------------------------------------------------------------------------------------------------------------------------------Prefix Sym SubmultipleScientificStandard Form -bol or multipleNotation----------------------------------------------------------------------------------------------------------------------------------YottaY10241.0x1024 1,000,000,000,000,000,000,000,000ZettaZ10211.0x10211,000,000,000,000,000,000,000ExaE10181.0x10181,000,000,000,000,000,000PetaP10151.0x10151,000,000,000,000,000TeraT10121.0x10121,000,000,000,000GigaG10091.0x10091,000,000,000MegaM10061.0x10061,000,000Kilok10031.0x10031,000Hectoh10021.0x1002100Dekada10011.0x100110Decid 10-11.0x10-10.1Centic10-21.0x10-20.01Millim10-31.0x10-30.001Microμ10-61.0x10-60.000001Nanon10-91.0x10-90.000000001Picop10-121.0x10-120.000000000001Femtof10-151.0x10-150.000000000000001Attoa10-181.0x10-180.000000000000000001Zeptoz10-211.0x10-210.000000000000000000001Yoctoy10-241.0x10-240.000000000000000000000001* Use prefixes only with the base units such as, meter, gram, second, pound, and yard.* The positive exponents indicate the no. of digits after unity or after the assumed location of the decimal point.* The negative exponents indicate the no. of digits the decimal point is to be placed to the left of unity.* To write a number in scientific form, use the formula: a x 10nWhere a (number sequence or significand whose absolute value) is equal to or greater than one (1) but less than ten (10), and 10n (the order of magnitude) where n is a positive or negative integer.Take for example, the velocity of light which is approximately 30,000,000 meters per second and the mass of the electron which is about 0.000000000000000000000000000911 gram. To write these two quantities in the form given is troublesome and space-consuming. To avoid this, abbreviations in powers of ten or prefixes are used. Thus, the velocity of light can now be written as,30,000,000ms=3 x 108 M106ms =3 x 108-6Mms30,000,000ms=3 x 102Mms=300Mms=300megameterssecondand the mass of electron as,0.000000000000000000000000000911 g=9.11 x 10-28g1 y10-24=9.11 x 10-28+24 yg=9.11x 10-4 yg=0.000911 yg(0.000911 yoctogram)Review Test:1.Who said that "heavy objects drop faster than a light one?"_______________________2.Why did people of early times were filled with fear and superstition? ____________________________________________________________3.Who concluded, through his experiment performed at the famous leaning tower of Pisa, that heavy objects do not fall faster than light objects? _________________________________4.What are the useful tools in the study of Physics?____________________________________________________________5.What is the first step in the study of Physics? ____________6.What is the very essence of measuring or measurement?_________________________7.What were the two handicaps that delayed the development of science? ___________________________________________________8.What are the two methods of measurement?____________________________________________________________9.What system of units is popular in English-speaking countries?10.What system of units is now known as the modernized version of the metric system? ______________________________________Exercises: Rewrite the following numbers in the scientific form and in power of ten prefixes, or vice versa:1.1250000 grams = ____________________________________________2.0.000000277 meter = ________________________________________3.1.207 micrograms = _________________________________________4.3.987 gigameters = _________________________________________5.1.705 nanoliters = _________________________________________6.2.77 x 10-9 attoseconds = __________________________________7.0.5550 meter = _____________________________________________8.1.246 exaseconds = _________________________________________9.0.000000000000000000000000005001megaliter= _______________________________________10.9.8199 dekameter/s2 = ______________________________________ Conversion of Units The conversion of units from one system to another requires knowledge on the difference or relationship existing between the systems of units with a certain quantity - mass, length, or time. You got to know how one unit of measurement is relatively smaller or bigger than the other. Knowing first the appropriate conversion factor is the initial step in the conversion process.The supplementary lines list some of the conversion factors when working with the fundamental physical quantities.Some Conversion FactorsLength1 m = 1000 mm = 100 cm = 0.001 km = 39.370079 in= 3.2808399 ft = 1.0936133 yd = 6.2137119 x 10-4 mi1 yd= 914.4 mm = 91.44 cm = 0.9144 m = 0.0009144 km = 36 in= 3 ft = 5.6818182 x 10-4 mi1 in = 25.4 mm = 2.54 cm = 0.0254 m = 0.0000254 km= 0.08333 ... yd = 1.5782828 x 10-5 mi1 mi= 1609344 mm = 160934.4 cm = 1609.344 m = 1.609344 km= 63360 in = 5280 ft = 1760 yd1 km= 1000000 mm = 100000 cm = 1000 m = 39370.079 in= 3280.8399 ft = 0.621371194 miMass1 kg= 1000 g = 0.001 metric ton = 1.1023113 x10-3 short ton= 35.273962 (avdp) oz = 2.2046226 (avdp) lb= 32.150737 (troy) oz = 2.6792289 (troy) lb1 (avdp) lb = 453.59237 g = 0.45359237 kg = 16 (avdp) oz= 0.00045359237 metric ton = 0.0005 short ton= 14.583333 (troy) oz = 1.2152778 (troy) lb1 metric ton = 1000000 g = 1000 kg = 1.1023113 short ton= 35273.962 (avdp) oz = 2204.6226 (avdp) lb= 32150.737 (troy) oz = 2679.2289 (troy) lbTime1 day= 86400 s = 1440 min = 24 hrs1 hr= 1/24 day = 60 min = 3600 s1 min= 1/1440 day = 1/60 hr = 60 s1 s = 1/86400 day = 1/3600 hr = 1/60 min* Actually knowing just one set of factors in each of the three fundamental quantities is enough. All you have to do is applying simple algebraic manipulation by getting the reciprocal. For example, you want to know how many inches there are in a centimeter. Of course, you know already that for every inch you have an equivalent of 2.54 cm, but reversing the situation is quite another story. The answer is not that hard, after all. Simply get the reciprocal of 2.54 - that is, 1/2.54. Doing this with a calculator you'll get 0.39370079. The answer reveals that a centimeter is just a fraction of an inch, or a centimeter is smaller than an inch.Example: Convert the following units of measurement as indicated1.500 mi kmSolution:Conversion Factor is, 1 mi = 1.609344 km or 1 km = 0.621371194 mi 1.609344 km500 mi = 500 mi ( ------------------ ) 1 mi = 804.672 km (Answer)2.97 m ftSolution:Conversion Factor needed is, 1 m = 3.2808399 ft or 1 ft = 0.3048 m 1 ft97 m = 97 m ( ------------- ) = 318.2415 ft 0.3048 m3.1000 g lb (avdp)Solution:Conversion Factor needed is, 1 lb = 453.59237 g 1 lb1000 g = 1000 g ( -------------- ) 453.59237 g = 2.2046226 lb4.5 (avdp) lb (avdp) ozSolution:Conversion Factor needed is, 1 lb = 16 oz 16 oz5 lb = 5 lb ( -------------- ) 1 lb= 80 oz5.2 metric tons (avdp) lbSolution:Conversion Factor: 1 ton = 2204.6226 lb 2204.6226 lb2 tons = 2 tons ( ----------------- ) 1 ton = 4409.2452 lb6.5 m/s mi/hrSolution:Conversion Factors: 1 mi = 1609.344 m and 1 hr = 3600 s m 1 mi 3600 s5 m/s = 5 --- ----------------- ------------------ s ( 1609.344 m ) ( 1 hr ) = 11.18468146 mi/hr or 11.1847 mi/hr* To determine the conversion factor of any derived quantity - area, volume, etc., simply calculate the square, cube, or the appropriate integral power of the corresponding fundamental quantity. For example, to determine how square inches there are in a square foot, simply use the conversion factor for length, 1 foot = 12 inches, then square the said conversion factor - that is, compute the square of 1 foot [(1 ft)2 = 1 ft2] and square of 12 inches [(12 inches)2 = 144 in2].7.Make a program that prompts for the length and width of a rectangular table in inches, compute the area, convert the computed area in square inches into square centimeters, and display on the screen the computed area in square inches and in square centimeters.Solution:{ This program calculates the area of a rectangle (based on its entered length and width), determine its equivalent in square centimeters, and displays on the screen the calculated area in square inches and in square centimeters. In addition, the program is designed to accomodate as many entries as the user desires. Conversion Factor needed is 1 inch = 2.54 cm} Program Area_of_a_Rectangle; Uses CRT; Var Len, Wid, Area, Sq_Cm :Real; More :Char; Begin Repeat ClrScr; GotoXY(27,07);Write(' The Area of a Rectangle '); {Entering the Length and Width of the Rectangle} GotoXY(20,10);Write('Enter the Length of the Rectangle in inches :'); ReadLn(Len); GotoXY(20,12);Write('Enter the Width of the Rectangle in inches :'); ReadLn(Wid); {Computing the Area of the Rectangle in square inches} Area := Len * Wid; {Converting the Area in square inches into square centimeters} Sq_Cm := Area * Sqr(2.54); {Displaying the Area in square inches and in square centimeters on the screen} GotoXY(30,14);Write('The Area is ',Area:7:2,' sq.in'); GotoXY(33,16);Write('or ',Sq_Cm:7:2,' sq. cm'); GotoXY(23,22);Write('Do you desire another entry [Y/N]? '); More :=UpCase(Readkey); Until More = 'N'; GotoXY(34,23);Write('Tapos man ...'); Delay(2000); End. {End of the Program}* The following Pascal program likewise illustrates conversion from one system of units to another:{ This simple menudriven program is a demo on how to translate a conversion process or formula in Physics into a computerreadable and computerexecutable instruction. This program in Pascal Language covers conversion of units in mass, length, and time.}Program Conversion_of_Units;Uses CRT;Type Str80 = String[80];VarTx:Str80;What:Char;Function CTxt(Var Tx :Str80):Byte;BeginCTxt := (80 Length(Tx)) Div 2 + 1End;Procedure Mass_Units;Var Mass, Gram, TOz, AOz, Kilo, MTon, STon :Real; Ans :Char;Begin Repeat ClrScr; Tx :=' Conversion on Mass Units '; GotoXY(CTxt(Tx),07);Write(Tx); GotoXY(22,10);Write('Enter Mass in Avoirdupois Pounds :'); ReadLn(Mass); Gram := Mass * 453.59237; GotoXY(22,12);Write('It''s equivalent to :'); GotoXY(30,14);Write(Gram:7:2,' Gram(s)'); TOz := Mass * 14.583333; GotoXY(30,15);Write(TOz:7:2,' Troy Ounce(s)'); AOz := Mass * 16; GotoXY(30,16);Write(AOz:7:2,' Avdp.Ounce(s)'); Kilo := Mass * 0.45359237; GotoXY(30,17);Write(Kilo:7:2,' Kilogram(s)'); STon := Mass / 2000; GotoXY(30,18);Write(STon:5:4,' Short Ton(s)'); MTon := Mass / 2204.6226; GotoXY(30,19);Write(MTon:5:4,' Metric Ton(s)'); Tx := 'Another try [Y/N]?'; GotoXY(CTxt(Tx),22);Write(Tx); Ans := UpCase(Readkey); Until Ans = 'N'; Tx :='Exiting from this procedure (submenu) ...'; GotoXY(CTxt(Tx),23);Write(Tx); Delay(1500)End;Procedure Length_Units;Var Len, inch, mm, cm, Ft, m, km, mi :Real; Response :Char;Begin Repeat ClrScr; Tx :='| Conversion on Length Units of Measure |'; GotoXY(CTxt(Tx),07);Write(Tx); GotoXY(25,10);Write('Enter Length in Yards :'); ReadLn(Len); GotoXY(25,12);Write('It''s equivalent to:'); mm := Len * 914.4; GotoXY(30,14);Write(mm:9:2,' Millimeter(s)'); cm := Len * 91.44; GotoXY(30,15);Write(cm:9:2,' Centimeter(s)'); inch := Len * 36; GotoXY(30,16);Write(Inch:7:4,' Inch(es)'); ft := Len * 3; GotoXY(30,17);Write(ft:7:4,' Foot(Feet)'); m := Len / 1.0936133; GotoXY(30,18);Write(m:6:5,' Meter(s)'); km := Len / 1093.6133; GotoXY(30,19);Write(km:5:6,' Kilometer(s)'); mi := Len / 1760; GotoXY(30,20);Write(mi:5:6,' Mile(s)'); Tx :='Do you desire another entry [Y/N]?'; GotoXY(CTxt(Tx),22);Write(Tx); Response := Upcase(ReadKey); Until Response = 'N'; Tx := 'Backing out ...'; GotoXY(CTxt(Tx),23);Write(Tx); Delay(1500);End;Procedure Time_Units;Var Time, Milli, Micro, Min, Hour, Day:Real; Ano :Char;Begin Repeat ClrScr; TextColor(Red+Blink);TextBackGround(Yellow); Tx := '| Conversion on Time Units of Measure |'; GotoXY(CTxt(Tx),07);Write(Tx); NormVideo; GotoXY(25,10);Write('Enter Time in Seconds :'); ReadLn(Time); GotoXY(25,12);Write('In the Units of :'); Milli := Time * 1000; Micro := Time * 1.0E+06; Min := Time / 60; Hour := Time / 3600; Day := Time / 86400; GotoXY(30,14);Write('Microseconds = ',Micro:9:2); GotoXY(30,15);Write('Milliseconds = ',Milli:9:2); GotoXY(30,16);Write('M i n u t e s = ',Min:6:5); GotoXY(30,17);Write('H o u r s = ',Hour:5:6); GotoXY(30,18);Write('D a y s = ',Day:4:7); Tx := 'Isa pa [Y/N]? '; GotoXY(CTxt(Tx),22);Write(Tx); Ano := UpCase(ReadKey); Until Not(Ano='Y'); Tx :='Leaving this procedure for the Main Menu ...'; GotoXY(CTxt(Tx),23);Write(Tx); Delay(1500);End;Begin (* Main Body of the Program *) RepeatClrScr; TextColor(Blue+Blink);TextBAckGround(White);Tx := ' Conversion of Units Program ';GotoXY(CTxt(Tx),03);Write(Tx); NormVideo;Tx := 'From English to S.I. Units, or Smaller/Bigger Units';GotoXY(CTxt(Tx),05);Write(Tx);GotoXY(30,08);Write('[ 1 ] M a s s');GotoXY(30,10);Write('[ 2 ] L e n g t h');GotoXY(30,12);Write('[ 3 ] T i m e');Tx := 'Which Quantity [1,2,3,Q=Quit] ( )';GotoXY(CTxt(Tx),15);Write(Tx);GotoXY(CTxt(Tx)+Length(Tx)3,15);What := UpCase(Readkey);Case What Of'1':Mass_Units;'2':Length_Units;'3':Time_Units;End; Until What = 'Q'; Tx := 'That''s it in the meantime ...'; TextColor(Black+Blink);TextBackground(White); GotoXY(CTxt(Tx),20);Write(Tx); Delay(1500); NormVideoEnd. (* The End of the Program *)Exercises. Convert the following quantities as indicated.1.5096 ft meters2.107.67 (avdp) lb kg3.1677 m yd4.1.979 Ms hr5.71100 micrometers inches6.100 mi/hr m/s7.50 lb/in2 g/cm28.200 kg/m3 lb/ft39.100 ft3 cm310.Make a program that would simulate a conversion process on any of the preceding numbers. The given value should be entered, conversion process should then follow, and finally the converted value should be shown on the screen. Vector & Scalar Quantities Scalar Quantities. Quantities in which direction is neither applicable (as in temperature) nor specified (as in speed). Some authors defined them as the physical quantities that require only a magnitude and a unit or measure. They obey the normal rules of algebra in addition, subtraction, multiplication, and division. Additional examples of this sort of physical quantities are resistance, time, mass, distance, energy, density, and volume. Vector Quantities. Quantities that require the specification of a magnitude, a unit of measure, and a direction. Some examples of this kind of physical quantities are force, velocity, field strength, displacement, acceleration, and luminous intensity. Three Important Parts of VectorArrowhead – indicates the direction of the vector.Length of the Arrow – represents the magnitude of the vector.Tail – represents the origin of the vector.Length of the Arrow2582545-9594850015773403810000TailArrowheadAddition of VectorsA. Vectors Acting in the Same DirectionThe resultant of two vectors acting in the same direction is a vector whose magnitude is equal to the sum of their magnitudes and acts in the same direction as they do.B. Vectors Acting in Opposite DirectionThe resultant of two vectors acting in opposite direction is a vector whose magnitude is equal to the difference of their magnitudes and which acts in the direction of the vector with greater magnitude.C. Vectors Acting in Any DirectionThe resultant of two vectors acting in any direction is a vector whose magnitude is the length of the line connecting the tail of the first and the head (tip) of the last and whose direction is the angle that the said line makes with the positive x-axis.Resultant. The sum of two or more vectors.General Methods of Finding the ResultantGraphical Methods. Methods Polygon Method. A method that uses a coordinate system or direction guide as a frame of reference.Parallelogram Method. A method that determines the resultant of two vectors at a time by determining the length of the longer diagonal of a formed a parallelogram.Analytical MethodsTrigonometric Method Using Cosine LawComponent MethodKinematics(Describing Motion)Kinematics. The branch of classical mechanics that describes the motion of points, bodies (objects) and systems of bodies (groups of objects) without consideration of the causes of motion. It applies geometry to the analysis of movement, or motion, of a mechanical system. (Wikipedia). It studies motion and the development of equations to describe motions of objects (wiseGEEK). Motion is a (continuous) change of position of an object with respect to time and a certain reference point. It is typically described in terms of displacement, direction, velocity, acceleration, and time. It is observed by attaching a frame of reference to a body and measuring its change in position relative to that frame (Wikipedia). It is relative – that is, an object can be moving with respect to one body and at the same time be at rest or be moving at different speed with respect to another body.When you are sitting in a bus traveling at 52 mph (miles per hour), you are moving with respect to the road, but not with respect to the seats, floor or walls of the bus. Your speed with respect to the road is 52 mph while with respect to that of the floor of the bus is zero. If another bus is traveling 52 mph should be coming toward you, your speed with respect to the bus would be 104 mph – that is, the speed of the bus you’re riding (52 mph) plus the speed of that bus (52 mph).Two Main Types of Motion According to the Speed and DirectionUniform Motion. A type motion in which both speed and direction of the moving object remain the same. It is therefore a type of motion at constant velocity (e.g., when you’re driving your car at a steady speed of 52 mph on a straight road).Accelerated Motion. A type of motion with changing velocity. Velocity changes when you keep changing your direction, speed, or both your direction and speed (e.g., when you oress the accelerator pedal of your car to increase its speed).Other Types of MotionSimple harmonic motion – (e.g. pendulum).Periodic motionRectilinear motion (Linear motion) – motion which follows a straight linear path, and whose displacement is exactly the same as its trajectory.Reciprocating (i.e. vibration)Brownian motion (i.e. the random movement of particles)Circular motion (e.g. the orbits of planets)Rotary motion – a motion about a fixed point. (e.g. Ferris wheel).Curvilinear motion – It is defined as the motion along a curved path that may be planar or in three dimensions.Rotational motionRolling motion - (e.g. the wheel of a bicycle)OscillationCombination motions - Combination of two or more above listed motionsPlanar Motion – the result of vectors summing to zero. This can be analyzed using plane geometry.Spherical Motion (rotation around a point) - the motion of a rigid body during which one of its points O remains fixed, while all the other points move along the surface of spheres with their center at point O.Spatial MotionDisplacement & DistanceDistance (farness). The numerical description of how far apart two objects are. It may refer to a physical length, or an estimation based on other criteria (e.g. "two counties over") (Wikipedia).Displacement. A vector that points from the object's initial position to its final position and whose magnitude equals the distance separating the points. It indicates the separation n of one point to another and direction of the separation.Displacement = final position - initial positiond = r2 - r1For a linear motion along a single axis, such as the x-axis,d = x2 - x1There is no use of vector symbols for displacement in one dimension because positive and negative signs suffice already.Speed and VelocitySpeed and velocity are similar quantities in that they both describe how fast an object moves. There is, however, a significant difference - velocity is a vector quantity that specifies both how fast and in what direction an object moves, whereas speed specifies only how fast the object moves.Average Speed, v. The distance traveled divided by the time required to travel that distance. Units of speed include km/h, m/s, mi/h, or any unit of distance divided by time.v = Distance Traveled Elapsed Time= d tExample:In 1926, Johnny Weissmuller set the men's world 400-m swimming record in 4 min, 57.0 s. In 1966, Martha Randall set the women's record in 4 min, 38.0 s. By how many meters would Martha have beaten Johnny if they had raced each other.Average Velocity (v) of an object during some time period is the object's displacement (a vector) during that time divided by the time. Its units are the same as that of speed.v = Displacement Elapsed TimeFor one-dimensional motion, we need only one axis (x axis or y axis) to indicate an object's position.v = Displacement along one axis Elapsed Time= x2 - x1t2 - t1= y2 - y1t2 - t1 Where x1 is the object's position along the axis at time t1 and x2 is its position at time t2.Example: An automobile moves along a straight track beside which are markers indicating the car's position at different times. If the car is at position x1 = 51.2 m at time t1 = 5.3 s and is at position x2 = 49.8 m at time t2 = 5.4 s, what is the car's velocity during that time interval?For two- or three-dimensional motion,v = Displacement in two or three dimensions Elapsed Time= r2 - r1t2 - t1 Instantaneous Speed and VelocityInstantaneous velocity indicates how fast an object moves at each instant of time and the direction of that motion. Instantaneous speed indicates only how fast an object is moving at each instant of time (e.g., the speedometer of an automobile).The instantaneous velocity of an object moving the x axis is its change in position Δx divided by the very short time Δt required for this change:v = Change in Position Change in Time= ?x?tIf the object moves in the positive x direction, Δx is positive, as is the velocity. If the object moves in the negative x direction, Δx and v are both negative. The instantaneous speed of the object is just the magnitude of v and is always a positive number with the appropriate unit of measure.Example: Determine the car's velocity undergoing a displacement of 4.3 m in a direction 33 North of East during a 0.15-s time interval.*** In the succeeding discussion, whenever the word speed is used it is understood to mean "instantaneous speed" and velocity to mean "instantaneous velocity."Acceleration. The rate of increase of speed or velocity. If its a decrease of speed or velocity it is called deceleration - the negative of acceleration).Average Acceleration, a, of an object is its change in velocity divided by the time required for that change:a = Change in Velocity Elapsed Time= v2 - v1t2 - t1Example 1: An automobile travelling east in the positive x direction at +25 m/s and needs to pass a truck. The automobile's velocity is increased to +35 m/s in 3 s and still in the same direction. Calculate its acceleration.Example 2: A car traveling east in the positive x direction at +75 ft/s comes up behind a large truck and is unable to pass. The car slows down to 60 ft/s in a time of 2 s. Determine its deceleration.An object's instantaneous acceleration, a, is its change in velocity Δv divided by the very short time Δt needed for that change.a = ?v?tTwo-Dimensional MotionProjectile. Any object projected into space (empty or not) by the exertion of a force.Delivery Projectiles. Projectiles that carry an explosive charge or another chemical or biological substance. Aside from explosive payload, a projectile can be designed to cause special damage, e.g. fire, or poisoning.Kinetic Projectiles. Projectiles that do not contain an explosive charge nor any other kind of charge. Other terms for this kind of projectiles are kinetic energy weapon, kinetic energy warhead, kinetic warhead or kinetic penetrator. A kinetic projectile can also be dropped from an aircraft.Trajectory. A path that a moving object follows through space as a function of time. The object might be a projectile or satellite. It thus includes the meaning of orbit – the path of a planet, an asteroid, or a comet as it travel around a central mass. A trajectory can be described mathematically either by the geometry of the path, or as the position of object over time. Procedure to Solving Problems in Kinematics The first step in solving most physics problems involves drawing a picture or diagram of the situation described in the problem. Include in the diagram (a) a drawing that represents your interpretation of what is happening, (b) a coordinate axis or axes, (c) the value of known quantities represented in terms of appropriate symbols, and (d) a symbol for the unknown quantity you wish to determine. The picture puts all the problem information in front of you in an easily accessible from and also gives you a better intuitive grasp of the problem.Divide and conquer. Some of the more complex and interesting problems of real life must be divided into parts. Each part can often be solved with relative ease even though the original problem might have seemed impossibly complicated.Find one of the kinematics equations in which the only unknown quantity in the equation is the one whose value you wish to calculate.Rearrange the equation so that the unknown appears alone on the left and the known quantities are on the right. You have much less chance of error if you rearrange the equation before you substitute known quantities.Substitute the values of the known quantities and calculate the value of the unknown, including its units.Check your work. Does your answer have the correct units? If not, you may have made a mistake in your algebraic manipulations. Does the magnitude of the answer seem reasonable?Example 1: The driver of a car traveling at 55 mph needs to quickly reduce the car’s speed to 35 mph to round a curve in the highway. If the car’s deceleration has a magnitude of 6.0 m/s?, how far does it travel while reducing its speed?Example 2: A pole vaulter after crossing the bar lands on a foam cushion. His downward speed as he first touches the cushion is 6.8 m/s, and he sinks 25 cm into the cushion before stopping. Estimate his acceleration, assumed constant, while being stopped by the cushion. Procedure to Solving Problems in Dynamics (Kinetics) 1.Make a drawing of the whole situation being considered. Identify as precisely as possible the known information and the unknown quantity you wish to determine.2.Construct a force (free-body) diagram for a particular object in your drawing. The force diagram allows to you focus you attention on one small part of a complicated situation. Usually all, or all but one, of the forces acting on this object are known. Draw arrows to represent each known and unknown force acting on the object. The object's acceleration is a consequence of the forces shown in the diagram and is not itself a force. Hence, the ma (or max or may ) of Newton's Second Law should not appear as a force in the diagram, although you should indicate the magnitude and direction of the acceleration if known.3.Superimpose a coordinate system on the force diagram developed in the preceding step. The coordinate system provides a set of axes along which you calculate a force component when solving the equations:ΣFx = F1x + F2x + F3x + ... = maxandΣFy = F1y + F2y + F3y + ... = mayYou may wish to move your vectors so that their tails are at the origin. This makes it easier to calculate their components. You can reduce the difficulty of solving a problem by orienting your coordinate axes in particular directions.4.Apply Newton's Second Law in component form to the problem.ΣFx =max, ΣFy =may5.Solve the equations for the unknowns. Often, you will also use kinematic equations (refer to four equations below) along with Newton's Second Law when solving for an unknown.Kinematics Equations:v = vo + atEq'n 1x - xo= v+vo2tEq'n 2 x - xo = vot + ? at?Eq'n 3 2a(x - xo) = v? - vo?Eq'n 4The last step in this problem-solving procedure usually proceeds in one of the ways - another divide and conquer approach. If all the forces acting on an object are known, we use Newton's second law to calculate the object's acceleration. Having found the acceleration, we can use kinematics to determine the future velocity and position of the object. Tension. A force exerted by a string, rope, or cable on an object to which it is attached. It pulls in the direction of the rope and is exerted uniformly along its entire length. Normal Force. A force exerted by one object to another object it gets in touch with. Its direction is always perpendicular (that is, 90) to the surface of contact. (In physics, the word normal means perpendicular.) Two objects exert normal forces on each other whenever they touch. Force (free-body) Diagram. A simplified sketch of a single object with force vectors drawn to represent every force acting on that object. It is a pictorial representation often used by physicists and engineers to analyze the forces acting on a body of interest.Accelerated Motion - GravitationalFree Falling Bodies. Bodies that the only force acting upon them is gravity. A free falling body is that which falls only under the action of gravity and no external force is applied on the body for its vertical motion. Or, a body whose motion is accelerated toward the center of the earth by the force of gravity, other forces acting on it being negligible by comparison. Free fall is an ideal state in which the only force to which something is subjected is the Earth’s gravitational attraction, or the hypothetical fall of a body such that the only force acting upon it is that of gravity.Two-Dimensional MotionProjectile. An object that can be fired or launched, e.g. an artillery shell or a rocket. Or, any object projected into space (empty or not) by the exertion of a force. Or, an object that moves through space under the influence of the Earth’s gravitational force. Two coordinates must be used to describe the projectile’s motion, since it moves horizontally as well as vertically.Projectile Motion. A form of motion where an object or particle (called a projectile) is thrown obliquely near the earth's surface, and it moves along a curved path under the action of gravity. The path followed by a projectile motion is called its trajectory. Projectile motion only occurs when there is one force applied at the beginning of the trajectory after which there is no interference apart from gravity. It is described in terms of motion in the horizontal x direction and independently by motion in the vertical y direction. If resistance can be ignored, the projectile’s horizontal motion continues at a constant velocity because horizontal acceleration is zero. The vertical motion, however, will have acceleration due to gravity.Projectile Motionx Equations (ax=0)y Equations (ay=-g)vx= vxo+axtWith ax=0,vx= vxovy= vyo+aytWith ay=-gvy= vyo-gtx- xo= ?vxo+ vxty- yo= ?vyo+ vytx- xo= vxot+?axtWith ax=0,x- xo= vxoty- yo= vyot+?aytWith ay=-gy- yo= vyot-?gt2axx- xo= vx2- vxo2 With ax=0,0= vx2- vxo22ayy- yo= vy2- vyo2 With ay=-g-2gy- yo= vy2- vyo2Gravitation. Universal force of attraction that acts between all bodies that have mass. Also known as gravitational attraction.Newton's Laws of Motion are three physical laws that together laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to said forces. They have been expressed in several different ways over nearly three centuries,[1] and can be summarized as follows:First Law: The Law of InertiaWhen viewed in an inertial reference frame, an object either is at rest or moves at a constant velocity, unless acted upon by a force. Inertia (resistance to change). The property of a body by which it remains at rest or continues moving in a straight line unless acted upon by a directional force.Second Law: The Law of AccelerationThe acceleration of a body is directly proportional to, and in the same direction as, the net force acting on the body, and inversely proportional to its mass. Thus, F?=?ma, where F is the net force acting on the object, m is the mass of the object and a is the acceleration of the object.Third Law: The Law of InteractionWhen one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction to that of the first body. This law indicates that forces always come in pairs - an action force and its reaction force. The action force is the force exerted by one object on another. The reaction force is the force exerted by the other object on the first. For example, rest your forearm against the edge of the pages of a book. Your arm exerts a force into and against the book. But the book also exerts a reaction force into and against your arm, as is apparent from the indentation of your skin and muscle at the region of contact.The three laws of motion were first compiled by Isaac Newton in his Philosophi? Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687.[4] Newton used them to explain and investigate the motion of many physical objects and systems.[5] For example, in the third volume of the text, Newton showed that these laws of motion, combined with his law of universal gravitation, explained Kepler's laws of planetary motion. 1: Draw the force diagram of a sand-loaded cart pulled upward by a 30-N force on a 30-degree inclined plane. The load weighs 200 lbs.Example 2: Determine the tension in a cable needed to lift a 2-ton elevator with an acceleration of 1.75 m/s?.Example 3: A quarter-pound baseball thrown by a fastball pitcher James Bankrupt was measured to have left his hand at an blazing speed of 125 miles per hour. (a) Determine the average acceleration of the while pushed forward in his hand a distance of 10 feet. (b) Calculate the average force of his hand on the ball during the said acceleration. Express your answers also in the S.I. Units. (Hint: Use kinematics equation 4 to solve for acceleration and kinetic equation by Newton's Second Law of Motion to solve for the force.)Example 5: A Boeing 707 jet with a takeoff mass of 107 metric tons has four engines each producing an average net thrust of 16900 lbs during takeoff. (a) Calculate the plane's average acceleration down the runway and (b) the distance it must travel on the runway to attain its 165 mi/hr liftoff speed. Ignore air resistance and other friction-type forces acting on the plane. Express your answers in the S.I. Units as well. (Hint: Use kinetic equation (Newton's 2nd Law of Motion) to solve for acceleration and kinematics equation 4 to solve for the distance.)Example 6: A car with an 175-lb driver collides into the back end of a parked cement mixer. The car and its driver, held in place by a seat belt and shoulder strap, stop 3.5 ft. from the point of impact. If the car's original speed was 60 ft/sec, determine the average force of the seat belt and shoulder strap on the driver. Express your answer in newtons. (Hint: Use kinematics equation 4 to solve for the deceleration, then use the x-component equation of Newton's 2nd Law to solve for the force).Example 7: A 65-kg stunt diver is to jump from a helicopter and land on an air cushion. His speed as he touches the cushion will be 27 m/s. To avoid injury, the average force of the cushion on his body while he is being stopped should be no more than 9400 N. Calculate the distance he must be able to sink into the cushion while being stopped by the cushion force. (Hint: Use Newton's 2nd Law y-component equation to solve for the acceleration and use the result to solve for the sinking distance (y - yo) with the appropriate kinematics equation.Example 8: Calculate the acceleration of a 37-kg kid on a skateboard rolling down a short hill inclined at 27 with the horizontal. Ignore rolling friction. (Hint: Simply use Newton's 2nd Law of Motion.)Example 9: A skier wishes to build a rope tow to pull herself up a ski hill that is at 17 with the horizontal. Determine the tension needed in the rope to give the skier's 69-kg body (including the skis on which she stands) a 1.27-m/s? acceleration. Ignore sliding friction.* Source :Physics: A General Intro by Alan Van HeuvelenStaticsStatics is the study of methods for quantifying the forces between bodies. Forces are responsible for maintaining balance and causing motion of bodies, or changes in their shape. You encounter a great number and variety of examples of forces every day, such as when you press a button, turn a doorknob, or run your hands through your hair. Motion and changes in shape are critical to the functionality of man-made objects as well as objects the nature. Friction Friction. The force that resists the motion of one surface relative to another with which it is in contact. For a body resting on a horizontal surface there is a normal contact force (FN) between the body and the surface, acting perpendicularly to the surface. If a horizontal force (Fy) is applied to a body with the intention of moving it right, there will be an equal horizontal friction force (Fs) to the left, resisting the motion. If Fy is increased until the body just moves, the value of Fs will also increase until it reaches the limiting frictional force (FL), which is the maximum value of Fs. FL is then equal to μsFN, where μs is the coefficient of static friction, the value of which depends on the nature of surfaces in contact with each other. Once the body is moving with constant velocity, the value of Fs falls to a value Fk, which is equal to μkFN, where μk is the coefficient of kinetic friction. Both μs and μk are independent of the surface area of the body unless this is very small and μk is almost independent of the relative velocity of the body and surface.The cause of friction is that surfaces, however smooth they may look to the eye, on the microscopic scale have many humps and crests. Therefore the actual area of contact is very small indeed, and the consequent very high pressure leads to local pressure welding of the surfaces. During the motion the welds are broken and remade continually.Rolling Friction. Friction between a rolling wheel and the plane surface on which it is rotating. As a result of small distortions of the two surfaces, the ideal line contact does not apply and there is a frictional force with a component, Fl, that opposes the motion. This component is proportional to the normal force FN according to the relationship Fr = μrFN, where μr is called the coefficient of rolling friction.Static Friction. A force existing between two surfaces in contact when there is no relative motion between them. Or a friction force that exists when on object does not slide along a surface on which it rests even though a force is exerted to make it slide. Its direction is parallel to the surface of contact and opposes the tendency to move. If we push a large box which is not moved by our push, we say that a static friction resists our efforts. This friction force is static because the box remains at rests, or "static," even though we push it.Factors that determine the maximum force that a static friction force can exert:1.The relative roughness of the two surfaces. A measure of the roughness of to surfaces is indicated by the coefficient of static friction μs of the surfaces. The larger the value of μs, the rougher the surfaces and the harder it is to make the object start sliding.2.The magnitude of the normal (perpendicular) force between the object and the surface on which it rests. The larger the normal force, the harder it is to make the object start sliding. Often, the magnitude of a normal force between an object and the surface on which it rests equals the object's weight. Thus, the greater the weight, the harder it is to make the object slide. However, the magnitude of the normal force does not always equal an object's weight.As a result of many experiments, it has been determined that the magnitude of the static friction force F s for relatively smooth surfacesis less than or equal to the product of the coefficient of static friction μs and the magnitude of the normal force F N between the surfaces:Fs μs FNThe direction of the static friction force F s is parallel to the surface of contact and opposes the tendency to move. Note that an object sitting at rest begins to slide if pulled or pushed by a force directed parallel to the surface whose magnitude exceeds the maximum possible static friction.Example: A 47-kg box rests on the floor. The coefficient of static friction between the box and the floor is 0.37. What magnitude of horizontal pushing force Fp is needed to make the box slide?Kinetic (Sliding) Friction. A friction force parallel to the surfaces in contact opposing the motion - that is, if an object slides across a surface, a kinetic friction force opposes its sliding. The word kinetic implies that the object is moving. A road, for example, exerts a kinetic friction force on a car that skids to a stop.After an object that is pushed or pulled starts to slide, less force is usually required to keep it sliding than was needed to start it sliding; that is, the kinetic friction is less than the maximum static friction force. The value of kinetic friction force depends not only on μk but also on the magnitude of the normal force between the two surfaces, just as the static friction does. From many experiments with relatively smooth surfaces, the magnitude of the kinetic friction force acting on an object sliding across a surface is given by the equation:Fk = μk FNThe coefficient of kinetic friction μk, is usually less than the coefficient of static friction. It is not actually constant for a surface because its value can depend on the condition of the surface and also on the speed with which one object moves across the other (that is, as long as the resultant heat does not alter the condition of the surface). Usually, the value of μk decreases slightly as the speed of the object increases. Kinetic and static frictions do not depend on the area of contact between surfaces. That is, when the surfaces are hard and cannot fold into little bulges and indentations of each other, friction forces are independent of area; however, if they can conform to each other's shape, the friction force does depend on area. Drag racers underinflate the rear tires of their cars so that the tires can fold into the bumps and valleys in a road. The back tires are also very wide to increase the area of contact between the tires and the road. This folding of wide tires into indentations of the road causes the friction between the road and the tire to increase, enabling the racer to start faster.Coefficients of Static (μs) and Kinetic (μk) FrictionSteel on Steel0.740.57Aluminum on Steel in Air0.600.50Aluminum on Aluminum in Air1.90...Copper on Steel0.530.36Brass on Steel0.510.44Zinc on Cast Iron0.850.21Copper on Cast Iron1.050.29Glass on Glass0.940.40Copper on Glass0.680.53Gold on Gold in Water Vapor2.50...Gold on Gold in Air2.80...Gold on Gold in Hydrogen Gasor Nitrogen Gas4.00...Teflon on Teflon0.040.04Teflon on Steel0.040.04Rubber on Concrete0.60 -1.00.80Rubber Tire on Concrete(Dry)1.000.70Rubber Tire on Concrete(Wet)0.700.50Wood on Wood0.25 - 0.50Ski Wax on Wet Snow0.10Ski Wax on Dry Snow0.04Greased Metals0.100.06Surfaces in Healthy Joint0.015Coefficients of Static Friction (μs) for Steel on SteelConditionμsDegassed in vacuum at high temperature(Welds on contact)Grease-free in vacuum0.78Grease-free in air0.39Clean and coated with light mineral oil0.23Clean and coated with castor oil0.15Clean and coated with stearic acid0.005 - 0.0132Example 1: A police, examining the scene of an accident, observes skid marks 30m long left by a 1200-kg car. The car skidded to a stop on a concrete highway having a coefficient of kinetic friction with the tires of 0.80. Estimate the car's speed at the beginning of the skid. (Hint: Find the normal force using the y-component equation of Newton's Second law, use the result to solve for the kinetic friction force, determine the deceleration of the car using the x-component equation of Newton's Second law, and finally, use kinematic equation 4 to calculate the velocity (vo) at the start of the skid.)Example 2: A 45-kg toboggan, including its load, it pulled along a horizontal surface covered with snow by the 127-N tension force of a rope directed 37 above the horizontal. If the coefficient of kinetic friction between the toboggan and the snow is 0.21, what time is required to increase the toboggan's speed from zero to 7 m/s? (Hint: Determine first the normal force (using the y-component equation of the Newton's 2nd law) and use its value to solve the kinetic friction force. Calculate the toboggan's acceleration using the x-component equation of Newton's 2nd law. Finally, calculate the time needed to increase its velocity from zero to 7 m/s, with the kinematic equation 1.Science is a broad grouping of disciplines containing many different areas that are all linked together by a single concept: the scientific method. The scientific method represents an investigative method based on observation, deduction, hypothesizing, and experimentation that can be applied to all areas of life. Though there are many ways to look at science, one of the most common is to divide it into three broad categories, each of which contains numerous subdisciplines: formal science, natural science, and social science. Formal science represents those disciplines that deal with symbols and theoretical ideas and their applications in the real world. Its inclusion as a science is often contested, but aspects of it are used in all other scientific disciplines. Formal science includes computer science, mathematics, and statistics.Natural science is the science that people usually think of when they hear the term. Those studying it use the scientific method to understand nature and the physical world. Natural science and its subdisciplines are sometimes referred to as “hard sciences” by their proponents, and it includes biology, chemistry, geology, and physics.Social science is the study of societies and the interactions within them, be they on a group or individual basis. It is sometimes referred to as a “soft science” by detractors. Social science includes anthropology, psychology, and sociology.Each broad scientific category contains many disciplines and subdisciplines with specific research foci. A few of these types of science for each category include the following:Formal Science DisciplinesComputer Science focuses on the processing of information in computers and other computational devices. Scientists develop new algorithms to process data, improve computer programming languages, and work with many other aspects of computers and programs that modern societies deal with daily.Mathematics is devoted to the representation and processing of quantities. While the mathematical expression “1 + 1 = 2” may seem simple, it is actually a complex concept filled with semantics. Aspects of mathematics are used by all of the other types of science.Statistics is the collection, analysis, and interpretation of data. While it can be used to find patterns, disprove theories, and make predictions, the science of statistics itself is not focused on any individual real world idea. Instead, the theories and laws in statistics can be applied to any properly formatted data. A Q-Test, for instance, can be used on data gathered from a chemistry, biology, or psychology experiment.Natural Science DisciplinesBiology is the scientific study of life. This can be very broad, such as how different species might have evolved over millions of years, or it can be very specific, such as what a specific animal eats. Biology has many subdisciplines including botany, entomology, and zoology.Chemistry studies matter, its states, and how it changes. What individual components things are made of, how they change when exposed to different temperatures, how they can be broken down, and how they can be rebuilt are all questions chemists often ask and try to solve. Subdisciplines of chemistry include biochemistry, food chemistry, inorganic chemistry, and organic chemistry.Physics is the study of matter, forces, and interactions, and it can be studied on a very large or small scale. The study of how planets and other stellar bodies interact is an example of physics done on a very large scale, while the study of subatomic particles represents physics on a small scale. Astronomy, electrodynamics, thermodynamics, and quantum mechanics are all subdisciplines of physics.Social Science DisciplinesAnthropology is the study of the origins, development, and uniqueness of human beings. It borrows from many other disciplines, and includes the branches of archeology, cultural anthropology, and physical anthropology. Psychology is the scientific study of thought and behavior. Understanding why people make the choices they do, how they deal with stress, and predicting what choices they will make in the future are all aspects of psychology. Analytical, behavioral, cognitive, and gestalt are all different schools of psychological thought and theory.Sociology is the scientific study of groups of people. How these groups interact with each-other, the rules of the groups (norms and laws), and how these groups are formed are all aspects that sociologists consider. ................
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