Chapter 1Chapter 1

The Physics Tool KitThe Physics Tool Kit

Objectives:Objectives: Explain need for standardization of Explain need for standardization of

measurementmeasurement Use metric systemUse metric system Convert measurementsConvert measurements Solve problems using length, area, and volumeSolve problems using length, area, and volume Distinguish between mass and weightDistinguish between mass and weight Use significant digits to determine accuracyUse significant digits to determine accuracy Differentiate between accuracy and precisionDifferentiate between accuracy and precision Solve problems using correct significant digitsSolve problems using correct significant digits Use a systematic approach to solving physics Use a systematic approach to solving physics

problemsproblems Analyze problems using the problem-solving Analyze problems using the problem-solving

methodmethod

Standards of MeasureStandards of Measure

Sets of units of measure for length, Sets of units of measure for length, weight, and other quantities defined in weight, and other quantities defined in a way that is useful to a large number a way that is useful to a large number of peopleof people

Many standards have been used Many standards have been used throughout historythroughout history

Introduction to the Metric Introduction to the Metric SystemSystem

SI (International System of Units of SI (International System of Units of Measurement) Measurement) ≈≈ metric system metric system

Gabriel Mouton credited for originating metric Gabriel Mouton credited for originating metric systemsystem

Decimal or base Decimal or base 1010 system (easy to use) system (easy to use)

Add prefixes to basic units Add prefixes to basic units

Can convert between simply by moving decimal Can convert between simply by moving decimal pointpoint

LengthLength Basic unit of length is Basic unit of length is metermeter (or metre as in (or metre as in

book); Abbreviated as “m”book); Abbreviated as “m”

Defined as the length of path traveled by light in Defined as the length of path traveled by light in a vacuum during a time interval of a vacuum during a time interval of 1/299,792,458 of a second1/299,792,458 of a second

For long distances, use kilometer = 1000 meters For long distances, use kilometer = 1000 meters (Similar to mile)(Similar to mile)

Short distances, use centimeter = 1/100 Short distances, use centimeter = 1/100 or a meter (Similar to inch)or a meter (Similar to inch)

Millimeter used to measure very small Millimeter used to measure very small distancesdistances

Conversion factor used to change from Conversion factor used to change from one set of units to another. Can also use one set of units to another. Can also use dimensional analysis.dimensional analysis.

Area and VolumeArea and Volume Equations for areas/volumes of different Equations for areas/volumes of different

shapes are found in inside back cover of shapes are found in inside back cover of book.book.

Be sure units are the same before you Be sure units are the same before you plug into equation.plug into equation.

The units for area on the result will be The units for area on the result will be squared, for example msquared, for example m²,², cm cm², ², or inor in². ². Area is the number of square units it Area is the number of square units it contains. contains.

The units for volume on the result will be The units for volume on the result will be cubed, i.e. mcubed, i.e. m³³, cm, cm³³, or in, or in³³..

Volume is the number of cubic units.Volume is the number of cubic units. V= LWH, or can use water displacement V= LWH, or can use water displacement

to measure. to measure.

When converting between units, be sure When converting between units, be sure to cube the conversion factor!to cube the conversion factor!

Mass and WeightMass and Weight Mass is the quantity of material making up an Mass is the quantity of material making up an

objectobject

Mass is constant!Mass is constant!

Basic unit of mass in metric system is kilogram Basic unit of mass in metric system is kilogram (1000 grams)(1000 grams)

A gram is defined as the mass of 1 cmA gram is defined as the mass of 1 cm³³ of water of water at its maximum density.at its maximum density.

For very small quantities, use milligram (1/1000 For very small quantities, use milligram (1/1000 of a gram).of a gram).

For very large quantities, use metric ton (1000 kg).For very large quantities, use metric ton (1000 kg).

Measure using a balance.Measure using a balance.

Weight is a measure of the gravitational force or Weight is a measure of the gravitational force or pull acting on an object.pull acting on an object.

Metric unit of weight is the Newton.Metric unit of weight is the Newton.

Measure using a spring balance.Measure using a spring balance.

TimeTime

Based on movement of the Earth and Based on movement of the Earth and the moon.the moon.

Basic unit of time is the second.Basic unit of time is the second.

BASIC UNITSBASIC UNITS

Physical QuantityPhysical Quantity English SystemEnglish System Metric SystemMetric System

MassMass Pound or slugPound or slug Gram or kilogramGram or kilogram

LengthLength inch, foot, yardinch, foot, yard Centimeter or Centimeter or metermeter

VolumeVolume Quart or gallonQuart or gallon Liter, milliliter, or cmLiter, milliliter, or cm33

TimeTime Hours, minutes, secondsHours, minutes, seconds SecondsSeconds

TemperatureTemperature Degrees FahrenheitDegrees Fahrenheit °C or Kelvin°C or Kelvin

Metric PrefixesMetric Prefixes

Kilo- hecto- deka- UNIT deci- centi- milli-

k h dk d c m

Move decimal point left Move decimal point right

Power of 10 between each increment

1. What is the prefix for .01?1. What is the prefix for .01?

1.1. DeciDeci

2.2. CentiCenti

3.3. MilliMilli

4.4. micromicro

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Figure 5.1:Figure 5.1: Comparison of Comparison of English and metric units.English and metric units.

Figure 5.2:Figure 5.2: Cube Cube

representations.representations.

Figure 5.3:Figure 5.3: A 100 mL A 100 mL graduated graduated cylinder.cylinder.

1 mL = 1 cm3

1 milliliter = 1 cubic centimeter

100 mL = 100 cm3

Significant Digits and AccuracySignificant Digits and Accuracy Exact numbers – number determined Exact numbers – number determined

by counting or definitionby counting or definition

Approximate numbers – number Approximate numbers – number determined by measurement or determined by measurement or estimationestimation

Accuracy – number of digits we are Accuracy – number of digits we are reasonably sure of having counted reasonably sure of having counted

Called Called significant digitssignificant digits

The greater the number of significant The greater the number of significant digits, the better the accuracydigits, the better the accuracy

See page 37 for determining the See page 37 for determining the number of significant digitsnumber of significant digits

Figure 5.5:Figure 5.5: Measuring a pin. Measuring a pin.

These divisions were visualized

Reading is between 2.8 cm & 2.9 cm

2.85 cm is measurement

“5” is uncertain

Significant FiguresSignificant Figures

Includes all numbers recorded in a Includes all numbers recorded in a measurementmeasurement

For pin, length = 2.85 cm: 3 significant For pin, length = 2.85 cm: 3 significant figuresfigures

All certain numbers plus first uncertainAll certain numbers plus first uncertain

Assume to be accurate to Assume to be accurate to ± 1 in last #± 1 in last # Pin length is 2.85 ± 0.01 cmPin length is 2.85 ± 0.01 cm Pin is somewhere between 2.84 & 2.86 cmPin is somewhere between 2.84 & 2.86 cm

PrecisionPrecision Precision – smallest unit with which Precision – smallest unit with which

measurement is made, or the position measurement is made, or the position of the last significant digitof the last significant digit

Accuracy is the number of Accuracy is the number of digits(significant). The greater the # digits(significant). The greater the # of digits, the better the accuracy.of digits, the better the accuracy.

Try not to confuse accuracy and Try not to confuse accuracy and precision (often have similar precision (often have similar meanings)meanings)

Calculations with MeasurementsCalculations with Measurements The sum or difference of measurements can be The sum or difference of measurements can be

no more no more precise precise than the least than the least preciseprecise measurementmeasurement

See rules for adding and subtracting top of page See rules for adding and subtracting top of page 4141

The product or quotient of measurements can The product or quotient of measurements can be no more be no more accurateaccurate than the least than the least accurateaccurate measurementmeasurement

See rules for multiplying and dividing top of See rules for multiplying and dividing top of page 42page 42

Units do not have to be the same to multiply and Units do not have to be the same to multiply and dividedivide

Units have to be the same to add or subtractUnits have to be the same to add or subtract

See rules for combining operations on page 43See rules for combining operations on page 43

Procedures in book based on methods followed by Procedures in book based on methods followed by American Association for Testing and MaterialsAmerican Association for Testing and Materials

This book will generally use three significant digitsThis book will generally use three significant digits

Problem-Solving MethodProblem-Solving Method

In technical fields, problem-solving is In technical fields, problem-solving is more than plugging numbers into more than plugging numbers into equationsequations

Understanding principle involved in Understanding principle involved in solving a problem more important solving a problem more important

Must be able to take data, analyze Must be able to take data, analyze problem, and find solution in orderly problem, and find solution in orderly mannermanner

Summary of Problem-Solving MethodSummary of Problem-Solving Method Read problem carefully (2 times)Read problem carefully (2 times) Make a sketch Make a sketch Write all given information – Write all given information – don’t forget don’t forget

units!units! Determine unknown – what are you trying to Determine unknown – what are you trying to

find outfind out Write basic equation or formula that relatesWrite basic equation or formula that relates Find working equation by solving basic Find working equation by solving basic

equation for unknownequation for unknown Substitute into equation – Substitute into equation – include units!include units! Work out equationWork out equation Check your answer – ask “Does this make Check your answer – ask “Does this make

sense?”sense?”

2. A new born baby usually is 2. A new born baby usually is about 45 ______ long about 45 ______ long

Km m cm mm

25% 25%25%25%1.1. KmKm

2.2. mm

3.3. cmcm

4.4. mmmm

1 2 3 4 5 6 7 8 9 10 11 12 13 14

3. 1 km is how many m?3. 1 km is how many m?

1 10100

1000

25% 25%25%25%1.1. 11

2.2. 1010

3.3. 100100

4.4. 10001000

1 2 3 4 5 6 7 8 9 10 11 12 13 14

4. 1 cm is how many mm?4. 1 cm is how many mm?

1 10100

1000

25% 25%25%25%1.1. 11

2.2. 1010

3.3. 100100

4.4. 10001000

1 2 3 4 5 6 7 8 9 10 11 12 13 14