Physics for Scientists and Physics for Scientists and EngineersEngineers

Introduction Introduction

andand

Chapter 1Chapter 1

PhysicsPhysics Fundamental ScienceFundamental Science

concerned with the basic principles of the concerned with the basic principles of the UniverseUniverse

foundation of other physical sciencesfoundation of other physical sciences Divided into major areas asDivided into major areas as

Classical MechanicsClassical Mechanics RelativityRelativity ThermodynamicsThermodynamics ElectromagnetismElectromagnetism OpticsOptics Quantum MechanicsQuantum Mechanics

Classical PhysicsClassical Physics

Mechanics and electromagnetism are basic Mechanics and electromagnetism are basic to all other branches of classical physicsto all other branches of classical physics

Classical physics developed before 1900Classical physics developed before 1900 Our study will start with Classical Our study will start with Classical

MechanicsMechanics Also called Newtonian MechanicsAlso called Newtonian Mechanics

Classical PhysicsClassical Physics

Includes MechanicsIncludes Mechanics Major developments by Newton, and continuing Major developments by Newton, and continuing

through the latter part of the 19through the latter part of the 19thth century century ThermodynamicsThermodynamics OpticsOptics ElectromagnetismElectromagnetism

All of these were not developed until the latter part All of these were not developed until the latter part of the 19of the 19thth century century

Modern PhysicsModern Physics

Began near the end of the 19Began near the end of the 19 thth century century Phenomena that could not be explained by Phenomena that could not be explained by

classical physicsclassical physics Includes theories of relativity and quantum Includes theories of relativity and quantum

mechanicsmechanics

Classical Mechanics TodayClassical Mechanics Today

Still important in many disciplinesStill important in many disciplines Wide range of phenomena that can be Wide range of phenomena that can be

explained with classical mechanicsexplained with classical mechanics Many basic principles carry over into other Many basic principles carry over into other

phenomenaphenomena Conservation Laws also apply directly to Conservation Laws also apply directly to

other areasother areas

Objective of PhysicsObjective of Physics

To find the limited number of To find the limited number of fundamental laws that govern natural fundamental laws that govern natural phenomenaphenomena

To use these laws to develop theories To use these laws to develop theories that can predict the results of future that can predict the results of future experimentsexperiments

Express the laws in the language of Express the laws in the language of mathematicsmathematics

Theory and ExperimentsTheory and Experiments

Should complement each otherShould complement each other When a discrepancy occurs, theory may be When a discrepancy occurs, theory may be

modifiedmodified Theory may apply to limited conditionsTheory may apply to limited conditions

Example: Newtonian Mechanics is confined to objects Example: Newtonian Mechanics is confined to objects traveling slowing with respect to the speed of lighttraveling slowing with respect to the speed of light

Try to develop a more general theoryTry to develop a more general theory

Quantities UsedQuantities Used

In mechanics, three In mechanics, three basic quantitiesbasic quantities are used are used LengthLength MassMass TimeTime

Will also use Will also use derived quantitiesderived quantities These are other quantities can be expressed in These are other quantities can be expressed in

terms of theseterms of these

Standards of QuantitiesStandards of Quantities

Standardized systemsStandardized systems agreed upon by some authority, usually a agreed upon by some authority, usually a

governmental bodygovernmental body SI – Systéme InternationalSI – Systéme International

agreed to in 1960 by an international agreed to in 1960 by an international committeecommittee

main system used in this textmain system used in this text

LengthLength

UnitsUnits SI – meter, mSI – meter, m

Defined in terms of a meter – the Defined in terms of a meter – the distance traveled by light in a vacuum distance traveled by light in a vacuum during a given timeduring a given time

Table 1.1, p. 5

MassMass

UnitsUnits SI – kilogram, kgSI – kilogram, kg

Defined in terms of a kilogram, based Defined in terms of a kilogram, based on a specific cylinder kept at the on a specific cylinder kept at the International Bureau of StandardsInternational Bureau of Standards

Table 1.2, p. 5

Standard KilogramStandard Kilogram

The National Standard Kilogram The National Standard Kilogram No. 20, an accurate copy of the No. 20, an accurate copy of the International Standard Kilogram International Standard Kilogram kept at Sèvres, France, is housed kept at Sèvres, France, is housed under a double bell jar in a vault under a double bell jar in a vault at the National Institute of at the National Institute of Standards and Technology. Standards and Technology.

TimeTime

UnitsUnits seconds, sseconds, s

Defined in terms of the oscillation Defined in terms of the oscillation of radiation from a cesium atomof radiation from a cesium atom

Table 1.3, p. 6

Number NotationNumber Notation

When writing out numbers with When writing out numbers with many digits, spacing in groups of many digits, spacing in groups of three will be usedthree will be used No commasNo commas

Examples:Examples: 25 100 25 100 5.123 456 789 125.123 456 789 12

Reasonableness of ResultsReasonableness of Results

When solving a problem, you need When solving a problem, you need to check your answer to see if it to check your answer to see if it seems reasonableseems reasonable

Reviewing the tables of Reviewing the tables of approximate values for length, approximate values for length, mass, and time will help you test mass, and time will help you test for reasonablenessfor reasonableness

Systems of MeasurementsSystems of Measurements

US CustomaryUS Customary everyday unitseveryday units Length is measured in feetLength is measured in feet Time is measured in secondsTime is measured in seconds Mass is measured in slugsMass is measured in slugs

often uses weight, in pounds, instead of mass often uses weight, in pounds, instead of mass as a fundamental quantityas a fundamental quantity

PrefixesPrefixes

Prefixes correspond to powers of 10Prefixes correspond to powers of 10 Each prefix has a specific nameEach prefix has a specific name Each prefix has a specific abbreviationEach prefix has a specific abbreviation

PrefixesPrefixes The prefixes The prefixes

can be used can be used with any base with any base unitsunits

They are They are multipliers of multipliers of the base unitthe base unit

Examples:Examples: 1 mm = 101 mm = 10-3-3 m m 1 mg = 101 mg = 10-3-3 g g

Model BuildingModel Building

A A modelmodel is a system of physical is a system of physical componentscomponents Identify the componentsIdentify the components Make predictions about the behavior of the Make predictions about the behavior of the

systemsystem The predictions will be based on interactions The predictions will be based on interactions

among the components and/oramong the components and/or Based on the interactions between the Based on the interactions between the

components and the environmentcomponents and the environment

Models of MatterModels of Matter Some Greeks Some Greeks

thought matter is thought matter is made of atomsmade of atoms

JJ Thomson (1897) JJ Thomson (1897) found electrons and found electrons and showed atoms had showed atoms had structurestructure

Rutherford (1911) Rutherford (1911) central nucleus central nucleus surrounded by surrounded by electronselectrons

Models of MatterModels of Matter

Nucleus has structure, containing Nucleus has structure, containing protons and neutronsprotons and neutrons Number of protons gives atomic numberNumber of protons gives atomic number Number of protons and neutrons gives Number of protons and neutrons gives

mass numbermass number Protons and neutrons are made up of Protons and neutrons are made up of

quarksquarks

Modeling TechniqueModeling Technique

Important technique is to build a Important technique is to build a model for a problemmodel for a problem Identify a system of physical Identify a system of physical

components for the problemcomponents for the problem Make predictions of the behavior of Make predictions of the behavior of

the system based on the interactions the system based on the interactions among the components and/or the among the components and/or the components and the environmentcomponents and the environment

DensityDensity

Density is an example of a Density is an example of a derivedderived quantityquantity

It is defined as mass per unit volumeIt is defined as mass per unit volume

Units are kg/mUnits are kg/m33

m

V

Table 1.5, p.9

Atomic MassAtomic Mass

The atomic mass is the total The atomic mass is the total number of protons and neutrons in number of protons and neutrons in the elementthe element

Can be measured in Can be measured in atomic mass atomic mass unitsunits, u, u 1 u = 1.6605387 x 101 u = 1.6605387 x 10-27-27 kg kg

Basic Quantities and Their Basic Quantities and Their DimensionDimension

Dimension has a specific meaning – it Dimension has a specific meaning – it denotes the physical nature of a denotes the physical nature of a quantityquantity

Dimensions are denoted with square Dimensions are denoted with square bracketsbrackets Length [L]Length [L] Mass [M]Mass [M] Time [T]Time [T]

Dimensional AnalysisDimensional Analysis

Dimensional Analysis is a technique to check Dimensional Analysis is a technique to check the correctness of an equation or to assist in the correctness of an equation or to assist in deriving an equationderiving an equation

Dimensions (Dimensions (length, mass, time, length, mass, time, combinationscombinations) can be treated as algebraic ) can be treated as algebraic quantities quantities add, subtract, multiply, divideadd, subtract, multiply, divide

Both sides of equation must have the same Both sides of equation must have the same dimensionsdimensions

SymbolsSymbols

The symbol used in an equation is not The symbol used in an equation is not necessarily the symbol used for its dimensionnecessarily the symbol used for its dimension

Some quantities have one symbol used Some quantities have one symbol used consistentlyconsistently For example, time is For example, time is tt virtually all the time virtually all the time

Some quantities have many symbols used, Some quantities have many symbols used, depending upon the specific situationdepending upon the specific situation For example, lengths may be For example, lengths may be xx,, yy,, zz,, rr,, dd,, hh, etc., etc.

Dimensional AnalysisDimensional Analysis

Given the equation: Given the equation: x = ½ at x = ½ at 22

Check dimensions on each side:Check dimensions on each side:

TheThe T2’s cancel, leaving cancel, leaving L for the for the dimensions of each sidedimensions of each side The equation is dimensionally correctThe equation is dimensionally correct

LTTL

L 2

2

Conversion of UnitsConversion of Units

When units are not consistent, you may When units are not consistent, you may need to convert to appropriate onesneed to convert to appropriate ones

Units can be treated like algebraic Units can be treated like algebraic quantities that can cancel each other quantities that can cancel each other outout

See the inside of the front cover of your See the inside of the front cover of your textbook for an extensive list of textbook for an extensive list of conversion factorsconversion factors

ConversionConversion

Always include units for every quantity, Always include units for every quantity, you can carry the units through the you can carry the units through the entire calculationentire calculation

Multiply original value by a ratio equal Multiply original value by a ratio equal to oneto one

ExampleExample

cm1.38in1cm54.2

in0.15

cm?in0.15

Significant FiguresSignificant Figures

A significant figure is one that is reliably A significant figure is one that is reliably knownknown

Zeros may or may not be significantZeros may or may not be significant Those used to position the decimal point are Those used to position the decimal point are

not significantnot significant To remove ambiguity, use scientific notationTo remove ambiguity, use scientific notation

In a measurement, the significant In a measurement, the significant figures include the first estimated digitfigures include the first estimated digit

Significant FiguresSignificant Figures

0.0075 m 0.0075 m has 2 significant figureshas 2 significant figures The leading zeros are placeholders onlyThe leading zeros are placeholders only Can write in scientific notation to show more Can write in scientific notation to show more

clearly: clearly: 7.5 x 10-7.5 x 10-33 m m for 2 significant figuresfor 2 significant figures 10.0 m 10.0 m has 3 significant figureshas 3 significant figures

The decimal point gives information about the The decimal point gives information about the reliability of the measurementreliability of the measurement

1500 m1500 m is ambiguous is ambiguous Use Use 1.5 x 101.5 x 1033 m m for 2 significant figuresfor 2 significant figures Use Use 1.50 x 101.50 x 1033 m m for 3 significant figuresfor 3 significant figures Use Use 1.500 x 101.500 x 1033 m m for 4 significant figuresfor 4 significant figures

Operations with Significant Operations with Significant Figures – Multiplying or DividingFigures – Multiplying or Dividing

When multiplying or dividing, the number of When multiplying or dividing, the number of significant figures in the final answer is the significant figures in the final answer is the same as the number of significant figures in the same as the number of significant figures in the quantity having the lowest number of significant quantity having the lowest number of significant figures.figures.

Example: Example: 25.57 m x 2.45 m = 62.6 m25.57 m x 2.45 m = 62.6 m22

The The 2.45 m2.45 m limits your result to 3 significant limits your result to 3 significant figuresfigures

Operations with Significant Figures – Operations with Significant Figures – Adding or SubtractingAdding or Subtracting

When adding or subtracting, the number of When adding or subtracting, the number of decimal places in the result should equal the decimal places in the result should equal the smallest number of decimal places in any smallest number of decimal places in any term in the sum.term in the sum.

Example: Example: 135 cm + 3.25 cm = 138 cm135 cm + 3.25 cm = 138 cm The The 135 cm 135 cm limits your answer to the units limits your answer to the units

decimal valuedecimal value

Operations With Significant Figures – Operations With Significant Figures – Summary Summary

The rule for addition and subtraction are The rule for addition and subtraction are different than the rule for multiplication and different than the rule for multiplication and divisiondivision

For adding and subtracting, the For adding and subtracting, the number of number of decimal placesdecimal places is the important is the important considerationconsideration

For multiplying and dividing, the For multiplying and dividing, the number of number of significant figuressignificant figures is the important is the important considerationconsideration

RoundingRounding

Last retained digit is increased by 1 if Last retained digit is increased by 1 if the last digit dropped is 5 or abovethe last digit dropped is 5 or above

Last retained digit remains as it is if the Last retained digit remains as it is if the last digit dropped is less than 5 last digit dropped is less than 5

If the last digit dropped is equal to 5, If the last digit dropped is equal to 5, the retained digit should be rounded to the retained digit should be rounded to the nearest even numberthe nearest even number

Saving rounding until the final result will Saving rounding until the final result will help eliminate accumulation of errorshelp eliminate accumulation of errors

Explain the problem with your own words.Explain the problem with your own words. Make a good picture describing the problemMake a good picture describing the problem Write down the given data with their units. Convert all Write down the given data with their units. Convert all

data into S.I. system.data into S.I. system. Identify the unknowns.Identify the unknowns. Find the connections between the unknowns and the Find the connections between the unknowns and the

data.data. Write the physical equations that can be applied to the Write the physical equations that can be applied to the

problem.problem. Solve those equations. Solve those equations. Check if the values obtained are reasonable Check if the values obtained are reasonable order of order of

magnitude and units.magnitude and units.

Problem solving tacticsProblem solving tactics

Reasonableness of ResultsReasonableness of Results

When solving a problem, you need to When solving a problem, you need to check your answer to see if it seems check your answer to see if it seems reasonablereasonable

Reviewing the tables of approximate Reviewing the tables of approximate values for length, mass, and time will values for length, mass, and time will help you test for reasonablenesshelp you test for reasonableness