Introduction General Physics (PHY 2170). I. Introduction ► Physics: fundamental science ...

IntroductiIntroductionon

General Physics (PHY 2170)

I. IntroductionI. Introduction

►Physics: fundamental sciencePhysics: fundamental science foundation of other physical sciencesfoundation of other physical sciences

►Divided into five major areasDivided into five major areas MechanicsMechanics ThermodynamicsThermodynamics ElectromagnetismElectromagnetism RelativityRelativity Quantum MechanicsQuantum Mechanics

1. Measurements1. Measurements

►Basis of Basis of testingtesting theories in science theories in science►Need to have consistent Need to have consistent systems of systems of

unitsunits for the measurements for the measurements►UncertaintiesUncertainties are inherent are inherent►Need Need rules for dealing with the rules for dealing with the

uncertaintiesuncertainties

Systems of MeasurementSystems of Measurement

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

governmental bodygovernmental body►SI -- SystSI -- Systééme Internationalme International

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

main system used in this coursemain system used in this course also called also called mksmks for the first letters in the for the first letters in the

units of the fundamental quantitiesunits of the fundamental quantities

Systems of MeasurementsSystems of Measurements

►cgscgs -- Gaussian system -- Gaussian system named for the first letters of the units it named for the first letters of the units it

uses for fundamental quantitiesuses for fundamental quantities

►US CustomaryUS Customary everyday units (ft, etc.)everyday units (ft, etc.) often uses weight, in pounds, instead of often uses weight, in pounds, instead of

mass as a fundamental quantitymass as a fundamental quantity

Basic Quantities and Their Basic Quantities and Their DimensionDimension

►Length [L]Length [L]►Mass [M]Mass [M]►Time [T]Time [T]

LengthLength

►UnitsUnits SI -- meter, mSI -- meter, m cgs -- centimeter, cmcgs -- centimeter, cm US Customary -- foot, ftUS Customary -- foot, ft

►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 time (1/299 792 458 s)during a given time (1/299 792 458 s)

MassMass

►UnitsUnits SI -- kilogram, kgSI -- kilogram, kg cgs -- gram, gcgs -- gram, g USC -- slug, slugUSC -- slug, slug

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

Why do we need standards?

Standard KilogramStandard Kilogram

Why is it hidden under two glass domes?

TimeTime

►UnitsUnits seconds, sseconds, s in all three systems in all three systems

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

(9 192 631 700 times frequency of light emitted)(9 192 631 700 times frequency of light emitted)

Time MeasurementsTime Measurements

US “Official” Atomic ClockUS “Official” Atomic Clock

2. Dimensional Analysis2. Dimensional Analysis

► DimensionDimension denotes the denotes the physical naturephysical nature of a of a quantity quantity

► Technique to Technique to check the correctnesscheck the correctness of an of an equationequation

► Dimensions (length, mass, time, Dimensions (length, mass, time, combinations) combinations) can be treated as algebraic can be treated as algebraic quantitiesquantities add, subtract, multiply, divideadd, subtract, multiply, divide quantities added/subtracted only if have same unitsquantities added/subtracted only if have same units

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

Dimensional AnalysisDimensional Analysis

► Dimensions for commonly used quantitiesDimensions for commonly used quantities

Length L m (SI)Area L2 m2 (SI)Volume L3 m3 (SI) Velocity (speed) L/T m/s (SI)Acceleration L/T2 m/s2 (SI)

Example of dimensional analysis Example of dimensional analysis

distance = velocity · time L = (L/T) · T

3. Conversions3. Conversions

►When When units are not consistentunits are not consistent, you may , you may need to need to convertconvert to appropriate ones to appropriate ones

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

1 mile = 1609 m = 1.609 km 1 ft = 0.3048 m = 30.48 cm1m = 39.37 in = 3.281 ft 1 in = 0.0254 m = 2.54 cm

Example 1Example 1. Scotch tape:. Scotch tape:

Example 2Example 2. Trip to Canada:. Trip to Canada:Legal freeway speed limit in Canada is 100 km/h.

What is it in miles/h?

h

miles

km

mile

h

km

h

km62

609.1

1100100

PrefixesPrefixes

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

Power Prefix Abbrev.

1015 peta P109 giga G106 mega M103 kilo k10-2 centi c10-3 milli m10-6 micro 10-9 nano n

Distance from Earth to nearest star 40 PmMean radius of Earth 6 MmLength of a housefly 5 mmSize of living cells 10 mSize of an atom 0.1 nm

Example: An aspirin tablet contains 325 mg of acetylsalicylic acid. Express this mass in grams.

Solution:Given:

m = 325 mg

Find:

m (grams)=?

Recall that prefix “milli” implies 10-3, so

4. Uncertainty in 4. Uncertainty in MeasurementsMeasurements

►There is uncertainty in There is uncertainty in every every measurementmeasurement, this uncertainty carries , this uncertainty carries over through the calculationsover through the calculations need a technique to account for this need a technique to account for this

uncertaintyuncertainty

►We will use rules for We will use rules for significant figuressignificant figures to approximate the uncertainty in to approximate the uncertainty in results of calculationsresults of calculations

Significant FiguresSignificant Figures

► A A significant figuresignificant figure is one that is is one that is reliably knownreliably known► All non-zero digits are significantAll non-zero digits are significant► Zeros are significant whenZeros are significant when

between other non-zero digitsbetween other non-zero digits after the decimal point and another significant after the decimal point and another significant

figurefigure can be clarified by using scientific notationcan be clarified by using scientific notation

4

4

4

1074000.10.17400

107400.1.17400

1074.117400

3 significant figures

5 significant figures

6 significant figures

Operations with Significant Operations with Significant FiguresFigures

► AccuracyAccuracy -- number of significant figures -- number of significant figures

► When multiplying or dividing, round the When multiplying or dividing, round the result to the same accuracy as the result to the same accuracy as the leastleast accurate measurementaccurate measurement

► When adding or subtracting, round the When adding or subtracting, round the result to the result to the smallest numbersmallest number of decimal of decimal places of any term in the sumplaces of any term in the sum

Example: 135 m + 6.213 m = 141 m

meter stick: cm1.0

rectangular plate: 4.5 cm by 7.3 cmarea: 32.85 cm2 33 cm2

2 significant figures

Example:

Example:

Order of MagnitudeOrder of Magnitude► Approximation based on a number of assumptionsApproximation based on a number of assumptions

may need to modify assumptions if more precise results may need to modify assumptions if more precise results are neededare needed

► Order of magnitude is the power of 10 that appliesOrder of magnitude is the power of 10 that applies

Example: John has 3 apples, Jane has 5 apples. Their numbers of apples are “of the same order of magnitude”

Question: McDonald’s sells about 250 million packages of fries every year. Placed back-to-back, how far would the fries reach?

Solution: There are approximately 30 fries/package, thus:

(30 fries/package)(250 . 106 packages)(3 in./fry) ~ 2 . 1010 in ~ 5 . 108 m,which is greater then Earth-Moon distance (4 . 108 m)!

II. Problem Solving StrategyII. Problem Solving Strategy

Slide 13

Fig. 1.7, p.14

Known: angle and one sideFind: another sideKey: tangent is defined via two sides!

mmdistheight

dist

buildingofheight

3.37)0.46)(0.39(tantan.

,.

tan

Problem Solving StrategyProblem Solving Strategy

►Read the problemRead the problem identify type of problem, principle identify type of problem, principle

involvedinvolved

►Draw a diagramDraw a diagram include appropriate values and coordinate include appropriate values and coordinate

systemsystem some types of problems require very some types of problems require very

specific types of diagramsspecific types of diagrams

Problem Solving cont.Problem Solving cont.

►Visualize the problemVisualize the problem► Identify informationIdentify information

identify the principle involvedidentify the principle involved list the data (given information)list the data (given information) indicate the unknown (what you are indicate the unknown (what you are

looking for)looking for)

Problem Solving, cont.Problem Solving, cont.

►Choose equation(s)Choose equation(s) based on the principle, choose an based on the principle, choose an

equation or set of equations to apply to equation or set of equations to apply to the problemthe problem

solve for the unknownsolve for the unknown

►Solve the equation(s)Solve the equation(s) substitute the data into the equationsubstitute the data into the equation include unitsinclude units

Problem Solving, finalProblem Solving, final

► Evaluate the answerEvaluate the answer find the numerical resultfind the numerical result determine the units of the resultdetermine the units of the result

► Check the answerCheck the answer are the units correct for the quantity being are the units correct for the quantity being

found?found? does the answer seem reasonable? does the answer seem reasonable?

► check order of magnitudecheck order of magnitude

are signs appropriate and meaningful?are signs appropriate and meaningful?