Physics, 4 Edition - University Of Houston

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Lecture OutlineChapter 1Physics, 4th EditionJames S. WalkerCopyright 2010 Pearson Education, Inc.

Chapter 1Introduction to PhysicsCopyright 2010 Pearson Education, Inc.

Units of Chapter 1 Physics and the Laws of Nature Units of Length, Mass, and Time Dimensional Analysis Significant Figures Converting Units Order-of-Magnitude Calculations Scalars and Vectors Problem Solving in PhysicsCopyright 2010 Pearson Education, Inc.

1-1 Physics and the Laws of NaturePhysics: the study of the fundamental laws of nature these laws can be expressed as mathematicalequations much complexity can arise from relatively simplelawsCopyright 2010 Pearson Education, Inc.

1-2 Units of Length, Mass, and TimeAssume that you step on your bathroom scale and that it reads 120The number alone is meaningless. It must be accompanied by the units120 lb is a very different reading from 120 kg!Conclusion: For every physical parameter we will need the appropriate unitsi.e. a standard by which we carry out the measurement by comparison to thestandard. Does this mean that we have to define units for all parameters?The answer is no. In mechanics we need to define only three parameters:These parameters are: Length , Time, and MassThey are known as: base quantitiesIn this book we use the International System of Units (SI)In this system the units for the base quantities are:ParameterUnit ht 2010 Pearson Education, Inc.mskg

The meterAearthCequator BIn 1792 the meter was defined to be one ten-millionthof the distance from the north pole to the equator.1m AB107Since 1983 the meter is defined as the lengthtraveled by light in vacuum during the timeinterval of 1/299792458 of a second. The reasonwhy this definition was adapted was that themeasurement of the speed of light had becomeextremely preciseCopyright 2010 Pearson Education, Inc.

The Second(1-5)Initially the second was defined as follows:124 60 60of the time it takes the earthto complete a full rotationabout its axis1 second The problem with this definition is that the length of the day is not constant asis shown in the figure. For this reason since 1967 the second is defined asthe time taken by 9192631770 light oscillations of a particularwavelength emitted by a cesium-133 atom. This definition is so precisethat it would take two cesium clocks 6000 years before their readings woulddiffer more than 1 second.Copyright 2010 Pearson Education, Inc.

The kilogramThe SI standard of mass is a platinum-iridium cylinder shown in the figure. Thecylinder is kept at the International Bureau of Weights and Measures near Parisand assigned a mass of 1 kilogram. Accurate copies have been sent to othercountries.(1-6)A Second Mass StandardThe carbon-12 atom, by international agreement, has been assigneda mass of 12 atomic mass units (u). The relation between the twounits is: 1u 1.66053886 x 10-27KgCopyright 2010 Pearson Education, Inc.

SummarySI units of length (L), mass (M), time (T):Length: the meterWas: one ten-millionth of the distance from the North Poleto the equatorNow: the distance traveled by light in a vacuum in1/299,792,458 of a secondMass: the kilogramOne kilogram is the mass of a particular platinum-iridiumcylinder kept at the International Bureau of Weights andStandards, Sèvres, France.Time: the secondOne second is the time for radiation from a cesium-133atom to complete 9,192,631,770 oscillation cycles.Copyright 2010 Pearson Education, Inc.

1-2 Units of Length, Mass, and TimeQ: What is the typical lifetime of a dog in SI units?20 years ? sCopyright 2010 Pearson Education, Inc.

1-2 Units of Length, Mass, and TimeCopyright 2010 Pearson Education, Inc.

1-3 Dimensional Analysis Any valid physical formula must be dimensionallyconsistent – each term must have the same dimensionsFrom the table:Distance velocity timeVelocity acceleration timeEnergy mass (velocity)2Copyright 2010 Pearson Education, Inc.

1-4 Significant Figures accuracy of measurements is limited significant figures: the number of digits in a quantity thatare known with certainty number of significant figures after multiplication ordivision is the number of significant figures in the leastknown quantityCopyright 2010 Pearson Education, Inc.

1-4 Significant FiguresExample:A tortoise travels at 2.51 cm/s for 12.23 s. How far doesthe tortoise go?Answer: 2.51 cm/s 12.23 s 30.7 cm (three significantfigures)Copyright 2010 Pearson Education, Inc.

1-4 Significant FiguresScientific Notation Leading or trailing zeroes can make it hard todetermine number of significant figures: 2500, 0.000036 Each of these has two significant figures Scientific notation writes these as a number from 1-10multiplied by a power of 10, making the number ofsignificant figures much clearer:2500 2.5 103If we write 2.50x103, it has three significant figures0.000036 3.6 x 10-5Copyright 2010 Pearson Education, Inc.

1-4 Significant FiguresRound-off error:The last digit in a calculated number may vary dependingon how it is calculated, due to rounding off of insignificantdigitsExample: 2.21 8% tax 2.3868, rounds to 2.39 1.35 8% tax 1.458, rounds to 1.46Sum: 2.39 1.46 3.85 2.21 1.35 3.56 3.56 8% tax 3.84Copyright 2010 Pearson Education, Inc.

1-5 Converting UnitsConverting feet to meters:1 m 3.281 ft(this is a conversion factor)Or: 1 1 m / 3.281 ft316 ft (1 m / 3.281 ft) 96.3 mNote that the units cancel properly – this is the key tousing the conversion factor correctly!Copyright 2010 Pearson Education, Inc.

1-6 Order-of-Magnitude CalculationsWhy are estimates useful?1. as a check for a detailed calculation – if your answeris very different from your estimate, you’ve probablymade an error2. to estimate numbers where a precise calculationcannot be doneQ: What is the weight of your classmate sitting to your left?Copyright 2010 Pearson Education, Inc.

1-7 Scalars and VectorsScalar – a numerical value. May be positive or negative.Examples: temperature, speed, heightVector – a quantity with both magnitude and direction.Examples: displacement (e.g., 10 feet north), force,magnetic fieldCopyright 2010 Pearson Education, Inc.

1-8 Problem Solving in PhysicsNo recipe or plug-and-chug works all the time, but hereare some guidelines:1. Read the problem carefully2. Sketch the system3. Visualize the physical process4. Strategize5. Identify appropriate equations6. Solve the equations7. Check your answer8. Explore limits and special casesCopyright 2010 Pearson Education, Inc.

Summary of Chapter 1 Physics is based on a small number of laws andprinciples Units of length are meters; of mass, kilograms; and oftime, seconds All terms in an equation must have the samedimensions The result of a calculation should have only as manysignificant figures as the least accurate measurementused in itCopyright 2010 Pearson Education, Inc.

Summary of Chapter 1 Convert one unit to another by multiplying by theirratio Order-of-magnitude calculations are designed to beaccurate within a power of 10 Scalars are numbers; vectors have both magnitudeand direction Problem solving: read, sketch, visualize, strategize,identify equations, solve, check, explore limitsCopyright 2010 Pearson Education, Inc.