#1 Introduction Notes 1.1 The Science of Physics 1.Three fundamental aspects of Physics: 1....

#1 IntroductionNotes 1.1 The Science of Physics1.Three fundamental aspects of Physics:

1. Describing the organization of the universe. matter and energy

2. Understanding the natural laws that govern the universe. belief that all events follow a set of laws

that do not change

3. Deducing and applying natural laws. science as a process

#1 Introduction The Science of Physics2. Matter -What is required to change the phase of matter?

3. Energy- What is required to change the position of the block?

*The universe consists of only matter and energy

4.Inquiry and 5.Observation

*We will explore Physics using inquiry through observation.

6. Inquiry

Three valuable things are learned by discovering the natural laws through inquiry:

1. It includes very practical knowledge.2. Once you know how something generally

works, you can often figure out how to make it work for you.

3. You will learn to solve real-life problems.

7.Using Problem Solving Techniques

Step 1 Determine what the problem asks

you to find out.Step 2

Identify the information you are given.

Step 3 Identify laws or relationships.

Step 4 Apply the given information and

the relationships.

8.Foundations of Physics Units

9. Development of Scientific Knowledge

Models, Evidence, Analysis and Theories

Development of Scientific Knowledge

10. Importance of Experiments We use experiments to test and evaluate theories.

1.2 Development of Scientific Knowledge

Scientific Evidence

Measurements and data Graphs and chartsImages and sketches

1.2 Development of Scientific Knowledge

Scientific Knowledge and the Solar System

Early civilizations believed the Earth was covered by a

dome on which the sun, stars and planets moved.

In the Middle Ages, people thought the

sun, stars and planets circled the

Earth.

Today we know the earth and planets

orbit the sun.

12.Physics is Useful

Engineering

Medicine and health professions

12. Physics is Useful Business and finance

Art, music, and food

12.Physics is Useful

The relationship between physics and other fields of science

13.Types of Observations and 13.Types of Observations and MeasurementsMeasurements

We makeWe make QUALITATIVEQUALITATIVE observations of reactions — observations of reactions — changes in color and physical state.changes in color and physical state.

We also makeWe also make QUANTITATIVE QUANTITATIVE MEASUREMENTSMEASUREMENTS, which involve , which involve numbersnumbers..UseUse SI unitsSI units — based on the — based on the

metric systemmetric system

SI 14.SI measurementSI 14.SI measurement Le Système international Le Système international

d'unitésd'unités The only countries that have The only countries that have

not not officiallyofficially adopted SI are adopted SI are Liberia (in western Africa) and Liberia (in western Africa) and Myanmar (a.k.a. Burma, in SE Myanmar (a.k.a. Burma, in SE Asia), but now these are Asia), but now these are reportedly using metric reportedly using metric regularlyregularly

Metrication is a process that Metrication is a process that does not happen all at once, does not happen all at once, but is rather a process that but is rather a process that happens over time. happens over time.

Among countries with non-Among countries with non-metric usage, the U.S. is the metric usage, the U.S. is the only country significantly only country significantly holding outholding out.. The U.S. officially The U.S. officially adopted SI in 1866.adopted SI in 1866.

Information from U.S. Metric Association

On 9/23/99, $125,000,000 Mars Climate Orbiter entered Mars’ atmosphere 100 km lower than planned and was destroyed by heat.

1 lb = 1 N

1 lb = 4.45 N

“This is going to be the cautionary tale that will be embedded into introduction to the metric system in elementary school, high school, and college science courses till the end of time.”

Standards of MeasurementStandards of Measurement

15. When we measure, we use a measuring tool 15. When we measure, we use a measuring tool to compare some dimension of an object to a to compare some dimension of an object to a standard.standard. For example, at one time the For example, at one time the

standard for length was the standard for length was the king’s foot. What are some king’s foot. What are some

problems with this standard?problems with this standard?

16.Stating a Measurement16.Stating a Measurement

In every measurement there is aIn every measurement there is a

Number Number followed by a followed by a

Unit Unit from a measuring devicefrom a measuring device

The number should also be as precise as the The number should also be as precise as the

measurement!measurement!

17. Quantitative Measurement Being quantitative in Physics requires measurements How tall is Ming Yao? How about his weight?

Height: 2.29 m (7 ft 6 in) Weight: 141 kg (310 lb)

Number + Unit

“thickness is 10.” has no physical meaning Both numbers and units necessary for any meaningful physical quantities

September 4, 2008

18.UNITS OF MEASUREMENT18.UNITS OF MEASUREMENT

Use Use SI unitsSI units — based on the metric — based on the metric systemsystem

Length Length

MassMass

VolumeVolume

TimeTime

TemperatureTemperature

______________________________

Kilogram, kgKilogram, kg

Seconds, sSeconds, s

Celsius degrees, ˚CCelsius degrees, ˚Ckelvins, Kkelvins, K

______________________________

19.Type QuantitiesMany things can be measured: distance,

speed, energy, time, force ……These are related to one another: speed

= distance / timeChoose three basic quantities:

LENGTH MASS TIME

Define other units in terms of these.

20.SI Unit for 3 Basic QuantitiesMany possible choices for units of Length,

Mass, Time (e.g. Yao is 2.29 m or 7 ft 6 in) In 1960, standards bodies control and

define Système Internationale (SI) unit as,

LENGTH: Meter MASS: Kilogram TIME: Second

September 4, 2008

21. Mass vs. Weight21. Mass vs. Weight Mass: Amount of Mass: Amount of

Matter (grams, Matter (grams, measured with a measured with a BALANCE)BALANCE)

Weight: Force Weight: Force exerted by the exerted by the mass, only mass, only present with present with gravity (pounds, gravity (pounds, measured with a measured with a SCALE)SCALE)

Can you hear Can you hear me now?me now?

22.Some Tools for 22.Some Tools for MeasurementMeasurement

Which tool(s) Which tool(s) would you use to would you use to measure:measure:

A.A. temperature temperature

B.B. volume volume

C.C. time time

D.D. weight weight

23.Fundamental Quantities and SI Units

September 4, 2008

Length meter m

Mass kilogram kg

Time second s

Electric Current ampere A

Thermodynamic Temperature kelvin K

Luminous Intensity candela cd

Amount of Substance mole mol

Why should we care about SI units? Mars Climate Orbiter: http://mars.jpl.nasa.gov/msp98/orbiterhttp://mars.jpl.nasa.gov/msp98/orbiter

24.SI Length Unit: MeterFrench Revolution

Definition, 17921 Meter = XY/10,000,0001 Meter = about 3.28 ft1 km = 1000 m, 1 cm =

1/100 m, 1 mm = 1/1000 mCurrent Definition of 1

Meter: the distance traveled by light in vacuum during a time of 1/299,792,458 second.

September 4, 2008

25.SI Time Unit: Second 1 Second is defined as “atomic clock”– time taken

9,192,631,700 oscillations of the light emitted by a 133Cs atom.

Defining unit precisely is a science (important for, for example, GPS): This clock will neither gain nor lose a second in 20 million years.

September 4, 2008

26.SI Mass Unit: Kilogram1 Kilogram – the mass of a

specific platinum-iridium alloy kept at International Bureau of Weights and Measures near Paris.

Copies are kept in all other countries.

Yao Ming is 141 kg, equivalent to weight of 141 pieces of the alloy cylinder.

September 4, 2008

# 2 Learning Check White Board or letters and record on paperIntroduction Quantities

Match Match L) lengthL) length M) mass M) mass V) V) volumevolume

____ A. A bag of tomatoes is 4.6 kg.____ A. A bag of tomatoes is 4.6 kg.

____ B. A person is 2.0 m tall.____ B. A person is 2.0 m tall.

____ C. A medication contains 0.50 g Aspirin.____ C. A medication contains 0.50 g Aspirin.

____ D. A bottle contains 1.5 L of water.____ D. A bottle contains 1.5 L of water.

M

L

M

V

# 3 Learning Check# 3 Learning Check : Units White Board or letters and record on paper

What are some U.S. units that are What are some U.S. units that are used to measure each of the used to measure each of the following?following?

A. length A. length

B. volume B. volume

C. weightC. weight

D. temperatureD. temperature

SolutionSolution Some possible answers areSome possible answers are

A.A. length length inch, foot, yard, mile inch, foot, yard, mile

B.B. volumevolume cup, teaspoon, gallon, pint, quartcup, teaspoon, gallon, pint, quart

C.C. weight weight ounce, pound (lb), tonounce, pound (lb), ton

D.D. temperature temperature FF

27. Metric Prefixes27. Metric Prefixes Kilo-Kilo- means 1000 of that unit means 1000 of that unit

1 kilometer (km) = 1000 meters (m)1 kilometer (km) = 1000 meters (m) Centi-Centi- means 1/100 of that unit means 1/100 of that unit

1 meter (m) = 100 centimeters (cm)1 meter (m) = 100 centimeters (cm) 1 dollar = 100 cents1 dollar = 100 cents

Milli-Milli- means 1/1000 of that unit means 1/1000 of that unit 1 Liter (L) = 1000 milliliters (mL)1 Liter (L) = 1000 milliliters (mL)

28. Metric Prefixes28. Metric Prefixes

Metric PrefixesMetric Prefixes

29.Prefixes for SI Units10x

PrefixSymb

olx=1

8 exa E

15 peta P12 tera T9 giga G6

megaM

3 kilo k

2

hectoh

1 deca da

September 4, 2008

3,000 m = 3 1,000 m = 3 103 m = 3 km 1,000,000,000 = 109 = 1G 1,000,000 = 106 = 1M 1,000 = 103 = 1k

141 kg = ? g 1 GB = ? Byte = ? MB

29.Prefixes for SI Units

September 4, 2008

10x Prefix

Symbol

x=-1

deci d

-2 centi c-3 milli m-6

microµ

-9 nano n-12 pico p

-15

femtof

-18 atto a

0.003 s = 3 0.001 s = 3 10-3 s = 3 ms 0.01 = 10-2 = centi 0.001 = 10-3 = milli 0.000 001 = 10-6 = micro 0.000 000 001 = 10-9 = nano 0.000 000 000 001 = 10-12

= pico = p 1 nm = ? m = ? cm 3 cm = ? m = ? mm

30. Prefixes

X1000Kilo

k X100Hecto

h X 10Deka

daBasic Units

Meter mGram gLiter L

1/100Centi

c 1/1000Millim

1/10Deci

d

31.Units of Length31.Units of Length ? kilometer (km) = 500 meters (m)? kilometer (km) = 500 meters (m)

2.5 meter (m) = ? centimeters (cm)2.5 meter (m) = ? centimeters (cm)

1 centimeter (cm) = ? millimeter (mm)1 centimeter (cm) = ? millimeter (mm)

1 nanometer (nm) = 1.0 x 101 nanometer (nm) = 1.0 x 10-9-9 meter meter

O—H distance =O—H distance =9.4 x 109.4 x 10-11 -11 mm9.4 x 109.4 x 10-9 -9 cmcm0.094 nm0.094 nm

O—H distance =O—H distance =9.4 x 109.4 x 10-11 -11 mm9.4 x 109.4 x 10-9 -9 cmcm0.094 nm0.094 nm

# 4 Learning Check : PrefixesWhite Board or letters and record on paper Select the unit you would use to measure Select the unit you would use to measure

1. Your height1. Your height

a) millimeters a) millimeters b) metersb) meters c) c) kilometerskilometers

2. Your mass2. Your mass

a) milligramsa) milligrams b) gramsb) grams c) kilograms c) kilograms

3. The distance between two cities3. The distance between two cities

a) millimetersa) millimeters b) metersb) meters c) kilometers c) kilometers

4. The width of an artery4. The width of an arterya) millimetersa) millimeters b) metersb) meters c) kilometers c) kilometers

Solution

1. Your height1. Your height

b) metersb) meters

2. Your mass2. Your mass

c) kilogramsc) kilograms

3. The distance between two cities3. The distance between two cities

c) kilometersc) kilometers

4. The width of an artery4. The width of an arterya) millimetersa) millimeters

# 5 Drawing of the Meterstick Equalities ( Both Sides )

State the same measurement in two State the same measurement in two different unitsdifferent units

lengthlength

10.0 in.10.0 in.

25.4 cm25.4 cm

# 6. Learning Check : PrefixesWhite Board or letters and record on paper

1. 1000 m = 1 1. 1000 m = 1 ______ a) mm b) km c) dma) mm b) km c) dm

2. 0.001 g = 1 2. 0.001 g = 1 ___ ___ a) mg b) kg c) dga) mg b) kg c) dg

3. 0.1 L = 1 3. 0.1 L = 1 ______ a) mL b) cL c) dLa) mL b) cL c) dL

4. 0.01 m = 1 ___ 4. 0.01 m = 1 ___ a) mm b) cm c) dma) mm b) cm c) dm

32. Conversion Factors32. Conversion Factors

Fractions in which the numerator and Fractions in which the numerator and denominator are EQUAL quantities denominator are EQUAL quantities expressed in different unitsexpressed in different units

Example: 1 in. = 2.54 cm

Factors: 1 in. and 2.54 cm 2.54 cm 1 in.

# 7 Learning Check: Conversion FactorsWhite Board or letters and record on paper

Write conversion factors that relate Write conversion factors that relate each of the following pairs of units:each of the following pairs of units:

1. Liters and mL1. Liters and mL

2. Hours and minutes2. Hours and minutes

3. Meters and kilometers3. Meters and kilometers

# 8. How many minutes are in 2.5 hours?White Board or letters and record on paper

Conversion factor

2.5 hr x 2.5 hr x 60 min 60 min = 150 min = 150 min

1 hr1 hr

cancel

By using dimensional analysis / factor-label method, By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the side up, and the UNITS are calculated as well as the

numbers!numbers!

# 9 :Sample ProblemWhite Board or letters and record on paper

You have $7.25 in your pocket in You have $7.25 in your pocket in quarters. How many quarters do quarters. How many quarters do you have?you have?

7.25 dollars 4 quarters7.25 dollars 4 quarters 1 dollar1 dollar

X = 29 quarters= 29 quarters

# 10 . Learning Check White Board or letters and record on paper

A rattlesnake is 2.44 m long. A rattlesnake is 2.44 m long. How long is the snake in cm?How long is the snake in cm?

a) a) 2440 cm2440 cm

b)b) 244 cm244 cm

c)c) 24.4 cm24.4 cm

# 11Learning Check White Board or letters and record on paper

How many seconds are in 1.4 days?

Unit plan: days hr min seconds

1.4 days x 24 hr x ?? 1 day

Solution

Unit plan: days hr min seconds

1.4 day x 24 hr x 60 min x 60 sec

1 day 1 hr 1 min

= 1.2 x 105 sec

Wait a minute!What is What is wrongwrong with the following setup? with the following setup?

1.4 day x 1.4 day x 1 day 1 day x x 60 min 60 min x x 60 sec60 sec

24 hr 1 hr 24 hr 1 hr 1 min1 min

33. English and Metric 33. English and Metric ConversionsConversionsIf you know ONE conversion for If you know ONE conversion for

each type of measurement, you each type of measurement, you can convert anything!can convert anything!

You must You must memorizememorize and use and use these conversions:these conversions:Mass: 454 grams = 1 poundMass: 454 grams = 1 poundLength: 2.54 cm = 1 inchLength: 2.54 cm = 1 inchVolume: 0.946 L = 1 quartVolume: 0.946 L = 1 quart

Other Unit System34.U.S. customary system: foot, slug, secondCgs system: cm, gram, secondWe will use SI units in this course, but it is useful to know conversions between systems.

1 mile = 1609 m = 1.609 km 1 ft = 0.3048 m = 30.48 cm

1 m = 39.37 in. = 3.281 ft 1 in. = 0.0254 m = 2.54 cm 1 lb = 0.465 kg 1 oz = 28.35 g 1 slug = 14.59 kg 1 day = 24 hours = 24 * 60 minutes = 24 * 60 * 60 seconds .

#12. Learning CheckLearning Check

An adult human has 4.65 L of blood. An adult human has 4.65 L of blood. How many gallons of blood is that?How many gallons of blood is that?

Unit plan: L qt gallon

Equalities: 1 quart = 0.946 L 1 gallon = 4 quarts

Your Setup:

35.Steps to Problem Solving35.Steps to Problem Solving

Read problemRead problem Identify data Identify data Make a unit plan from the initial unit to Make a unit plan from the initial unit to

the desired unitthe desired unit Select conversion factorsSelect conversion factors Change initial unit to desired unitChange initial unit to desired unit Cancel units and checkCancel units and check Do math on calculator Do math on calculator Give an answer using significant figuresGive an answer using significant figures

#13. Dealing with Two Units – #13. Dealing with Two Units – Honors OnlyHonors Only

If your pace on a treadmill is 65 If your pace on a treadmill is 65 meters per minute, how many meters per minute, how many seconds will it take for you to walk a seconds will it take for you to walk a distance of 8450 feet?distance of 8450 feet?

Solution

InitialInitial

8450 ft x 8450 ft x 12 in. 12 in. x x 2.54 cm 2.54 cm x x 1 m 1 m

1 ft1 ft 1 in. 1 in. 100 100 cmcm

x x 1 min 1 min x x 60 sec 60 sec = 2400 sec = 2400 sec 65 m65 m 1 min 1 min

36.Unit Conversion Example: Is he speeding ?

On the garden state parkway of New Jersey, a car is traveling at a speed of 38.0 m/s. Is the driver exceeding the speed limit?

Put 1’s using unit conversion relations, as many times as necessary.

Multiply or divide numbers and units. Begin with 38.0 m/s = (38.0 m/s) 1 Since 1 mile = 1609 m, so we have 1 = 1 mile/1609 m

Then

Finally

smiles

mile

m

mile

s

m/1036.2

1600

0.38)

1609

1()0.38( 2

hrmilehr

mile

hr

mile

miles

s

mile

s

mile

/0.8560601036.21

min60

min601036.2

min601036.2

min1

601036.21036.2

22

222

37.What about Square and Cubic 37.What about Square and Cubic units? – Honors Onlyunits? – Honors Only

Use the conversion factors you Use the conversion factors you already know, but when you square already know, but when you square or cube the unit, don’t forget to cube or cube the unit, don’t forget to cube the number also!the number also!

Best way: Square or cube the Best way: Square or cube the ENITRE conversion factorENITRE conversion factor

Example: Convert 4.3 cmExample: Convert 4.3 cm33 to mm to mm33

4.3 cm4.3 cm33 10 mm 10 mm 33

1 cm 1 cm ( ) =

4.3 cm4.3 cm33 10 1033 mm mm33

1133 cm cm33

= 4300 mm3

# 14. Learning Check# 14. Learning Check

A Nalgene water A Nalgene water bottle holds 1000 bottle holds 1000 cmcm33 of of dihydrogen dihydrogen monoxide monoxide (DHMO). How (DHMO). How many cubic many cubic decimeters is decimeters is that?that?

SolutionSolution

1000 cm1000 cm33 1 dm 1 dm 33

10 cm10 cm( ) = 1 dm= 1 dm33

So, a dmSo, a dm33 is the same as a Liter ! is the same as a Liter !

A cmA cm33 is the same as a milliliter. is the same as a milliliter.

Experiment 1:Speed On paper : Purpose – Determine the length from

point A to point B in meters, in kilometers, in feet and miles .

Determine the elapsed time to cover the distance by walking, by running from point A to point B in sec .

calculate the speed in meters/sec, km/hr, miles/h

Experiment 2 : Density On paper Purpose : Determine the mass of the at

least three masses in grams(g), kilograms(kg), pounds(lbs)

Determine the volume of the cylinder in cm3, mL, Liters.

Calculate the density in g/cm3, g/ml, kg/L.

Textbook Examples : P 13 P12 P14 P15

38. Temperature 38. Temperature ScalesScalesFahrenheitFahrenheitCelsiusCelsiusKelvinKelvin

Anders Celsius1701-1744

Lord Kelvin(William Thomson)1824-1907

39.Temperature Scales39.Temperature Scales

Notice that 1 kelvin = 1 degree Celsius1 kelvin = 1 degree Celsius

Boiling point Boiling point of waterof water

Freezing point Freezing point of waterof water

CelsiusCelsius

100 ˚C100 ˚C

0 ˚C0 ˚C

100˚C100˚C

KelvinKelvin

373 K373 K

273 K273 K

100 K100 K

FahrenheitFahrenheit

32 ˚F32 ˚F

212 ˚F212 ˚F

180˚F180˚F

Calculations Using Calculations Using TemperatureTemperature

Generally require temp’s in Generally require temp’s in kelvinskelvins

T (K) = t (˚C) + 273.15T (K) = t (˚C) + 273.15Body temp = 37 ˚C + 273 = 310 KBody temp = 37 ˚C + 273 = 310 K

Liquid nitrogen = -196 ˚C + 273 = 77 KLiquid nitrogen = -196 ˚C + 273 = 77 K

Generally require temp’s in Generally require temp’s in kelvinskelvins

T (K) = t (˚C) + 273.15T (K) = t (˚C) + 273.15Body temp = 37 ˚C + 273 = 310 KBody temp = 37 ˚C + 273 = 310 K

Liquid nitrogen = -196 ˚C + 273 = 77 KLiquid nitrogen = -196 ˚C + 273 = 77 K

40.Fahrenheit Formula – Honors Only40.Fahrenheit Formula – Honors Only

180°F180°F = = 9°F 9°F == 1.8°F 1.8°F 100°C 100°C 5°C 5°C 1°C1°C

Zero point: 0°C = 32°FZero point: 0°C = 32°F

°F = 9/5 °C + 32°F = 9/5 °C + 32

41.Celsius Formula – Honors Only41.Celsius Formula – Honors Only

Rearrange to find T°CRearrange to find T°C

°F °F = = 9/5 °C + 329/5 °C + 32

°F - 32 = °F - 32 = 9/5 °C ( +32 - 32)9/5 °C ( +32 - 32)

°F - 32°F - 32 = = 9/5 °C9/5 °C

9/5 9/5 9/5 9/5

(°F - 32) * 5/9 = (°F - 32) * 5/9 = °C°C

42.Temperature Conversions – Honors 42.Temperature Conversions – Honors OnlyOnly

A person with hypothermia has a body A person with hypothermia has a body temperature of 29.1°C. What is the body temperature of 29.1°C. What is the body temperature in °F? temperature in °F?

°F °F = = 9/5 (29.1°C) + 329/5 (29.1°C) + 32

= = 52.4 + 3252.4 + 32

= = 84.4°F84.4°F

# 15. Learning Check – Honors Only# 15. Learning Check – Honors Only

The normal temperature of a chickadee is The normal temperature of a chickadee is 105.8°F. What is that temperature in °C?105.8°F. What is that temperature in °C?

1) 73.8 °C 1) 73.8 °C

2) 58.8 °C2) 58.8 °C

3) 41.0 °C3) 41.0 °C

#16. Learning Check – Honors Only

Pizza is baked at 455°F. What is that in °C?

1) 437 °C1) 437 °C

2) 235°C2) 235°C

3) 221°C3) 221°C

43. What is Scientific 43. What is Scientific Notation?Notation?

Scientific notation is a way of Scientific notation is a way of expressing really big numbers expressing really big numbers or really small numbers.or really small numbers.

It is most often used in It is most often used in “scientific” calculations where “scientific” calculations where the analysis must be very the analysis must be very precise.precise.

For very large and very small For very large and very small numbers, scientific notation is numbers, scientific notation is more concise.more concise.

44. Scientific notation 44. Scientific notation consists of two parts:consists of two parts:

A number between 1 and 10A number between 1 and 10

A power of 10A power of 10

N x 10N x 10xx

Are the following in scientific notation?

45.To change standard form 45.To change standard form to scientific notation…to scientific notation… Place the decimal point so that there Place the decimal point so that there

is one non-zero digit to the left of the is one non-zero digit to the left of the decimal point.decimal point.

Count the number of decimal places Count the number of decimal places the decimal point has “moved” from the decimal point has “moved” from the original number. This will be the the original number. This will be the exponent on the 10.exponent on the 10.

If the original number was less than If the original number was less than 1, then the exponent is negative. If 1, then the exponent is negative. If the original number was greater than the original number was greater than 1, then the exponent is positive.1, then the exponent is positive.

46. Examples46. ExamplesGiven: 289,800,000Given: 289,800,000Use: 2.898 (moved 8 places)Use: 2.898 (moved 8 places)Answer:Answer: 2.898 x 102.898 x 1088

Given: 0.000567Given: 0.000567Use: 5.67 (moved 4 places)Use: 5.67 (moved 4 places)Answer:Answer: 5.67 x 105.67 x 10-4-4

47.To change scientific 47.To change scientific notation to standard form…notation to standard form…Simply move the decimal Simply move the decimal

point to the right for positive point to the right for positive exponent 10. exponent 10.

Move the decimal point to the Move the decimal point to the left for negative exponent 10.left for negative exponent 10.

(Use zeros to fill in places.)(Use zeros to fill in places.)

48. Example48. ExampleGiven: 5.093 x 10Given: 5.093 x 1066

Answer: Answer: 5,093,0005,093,000 (moved 6 (moved 6 places to the right)places to the right)

Given: 1.976 x 10Given: 1.976 x 10-4-4

Answer: Answer: 0.00019760.0001976 (moved 4 (moved 4 places to the left)places to the left)

#17.Learning Check

Express these numbers in Express these numbers in Scientific Notation:Scientific Notation:

1)1) 405789405789

2)2) 0.0038720.003872

3)3) 30000000003000000000

4)4) 22

5)5) 0.4782600.478260

Three Three targets with targets with three arrows three arrows each to each to shoot.shoot.

Can you hit the bull's-eye?Can you hit the bull's-eye?

Both accurate and precise

Precise but not accurate

Neither accurate nor precise

How do How do they they compare?compare?

Can you define accuracy and precision?Can you define accuracy and precision?

49. Significant Figures49. Significant Figures

The numbers reported in a The numbers reported in a measurement are limited by the measurement are limited by the measuring toolmeasuring tool

Significant figures in a Significant figures in a measurement include the known measurement include the known digits plus one estimated digitdigits plus one estimated digit

50.Counting Significant FiguresCounting Significant Figures

RULE 1. All non-zero digits in a measured RULE 1. All non-zero digits in a measured number are significant. Only a zero could number are significant. Only a zero could indicate that rounding occurred.indicate that rounding occurred.

Number of Significant Figures

38.15 cm38.15 cm 44

5.6 ft5.6 ft 22

65.6 lb65.6 lb ______

122.55 m122.55 m ___

51. Leading Zeros51. Leading Zeros

.RULE 2. Leading zeros in decimal numbers RULE 2. Leading zeros in decimal numbers

are are NOTNOT significant. significant.


0.008 mm0.008 mm 11

0.0156 oz0.0156 oz 33

0.0042 lb0.0042 lb ________

0.000262 mL 0.000262 mL ____

52.Sandwiched Zeros52.Sandwiched Zeros

RULE 3. Zeros between nonzero numbers are RULE 3. Zeros between nonzero numbers are

significant. (They can not be rounded unless they significant. (They can not be rounded unless they

are on an end of a number.)are on an end of a number.)


50.8 mm50.8 mm 33

2001 min2001 min 44

0.702 lb0.702 lb ________

0.00405 m0.00405 m ____

53.Trailing Zeros53.Trailing Zeros

RULE 4. Trailing zeros in numbers without RULE 4. Trailing zeros in numbers without

decimals are NOT significant. They are decimals are NOT significant. They are

only serving as place holders.only serving as place holders. Number of Significant Figures

25,000 in. 25,000 in. 22

200. yr200. yr 33

48,600 gal48,600 gal ________

25,005,000 g 25,005,000 g ________

#18. Learning Check#18. Learning Check

A. Which answers contain 3 significant figures?A. Which answers contain 3 significant figures?

1) 0.47601) 0.4760 2) 0.00476 2) 0.00476 3) 4760 3) 4760

B. All the zeros are significant inB. All the zeros are significant in

1) 0.00307 1) 0.00307 2) 25.300 2) 25.300 3) 2.050 x 10 3) 2.050 x 1033

C. 534,675 rounded to 3 significant figures isC. 534,675 rounded to 3 significant figures is

1) 535 1) 535 2) 535,000 2) 535,000 3) 5.35 x 10 3) 5.35 x 1055

#19.Learning Check#19.Learning Check

In which set(s) do both numbers In which set(s) do both numbers contain the contain the samesame number of number of significant figures?significant figures?

1) 22.0 and 22.00 1) 22.0 and 22.00

2) 400.0 and 40 2) 400.0 and 40

3) 0.000015 and 150,0003) 0.000015 and 150,000


State the number of significant figures in each State the number of significant figures in each of the following:of the following:

A. 0.030 mA. 0.030 m 1 1 2 2 3 3

B. 4.050 LB. 4.050 L 2 2 3 3 4 4

C. 0.0008 gC. 0.0008 g 1 1 2 2 4 4

D. 3.00 mD. 3.00 m 1 1 2 2 3 3

E. 2,080,000 beesE. 2,080,000 bees 3 3 5 5 7 7

54.Significant Numbers in Calculations54.Significant Numbers in Calculations

A calculated answer cannot be more A calculated answer cannot be more precise than the measuring tool. precise than the measuring tool.

A calculated answer must match the least A calculated answer must match the least precise measurement.precise measurement.

Significant figures are needed for final Significant figures are needed for final answers fromanswers from

1) adding or subtracting1) adding or subtracting

2) multiplying or dividing2) multiplying or dividing

55. Adding and Subtracting55. Adding and SubtractingThe answer has the same number of The answer has the same number of decimal places as the measurement with decimal places as the measurement with the fewest decimal places.the fewest decimal places.

25.25.22 one decimal placeone decimal place

+ 1.+ 1.3434 two decimal placestwo decimal places

26.5426.54

answer 26.5answer 26.5 one decimal placeone decimal place

#21. Learning Check#21. Learning Check In each calculation, round the answer to In each calculation, round the answer to the correct number of significant figures.the correct number of significant figures.

A. 235.05 + 19.6 + 2.1 = A. 235.05 + 19.6 + 2.1 =

1) 256.751) 256.75 2) 256.8 2) 256.8 3) 2573) 257

B. 58.925 - 18.2B. 58.925 - 18.2 ==

1) 40.7251) 40.725 2) 40.73 2) 40.73 3) 40.73) 40.7

55. Multiplying and Dividing

Round (or add zeros) to the Round (or add zeros) to the calculated answer until you have the calculated answer until you have the same number of significant figures same number of significant figures as the measurement with the fewest as the measurement with the fewest significant figures.significant figures.


A. 2.19 X 4.2 =A. 2.19 X 4.2 = 1) 91) 9 2) 9.2 2) 9.2 3) 9.1983) 9.198

B. 4.311 ÷ 0.07 =B. 4.311 ÷ 0.07 = 1)1) 61.5861.58 2) 62 2) 62 3) 603) 60

C. C. 2.54 X 0.00282.54 X 0.0028 = = 0.0105 X 0.060 0.0105 X 0.060 1) 11.31) 11.3 2) 112) 11 3) 0.041 3) 0.041

53.Reading a Meterstick53.Reading a Meterstick

. l. l22. . . . I . . . . I. . . . I . . . . I33 . . . .I . . . . I . . . .I . . . . I44. . cm. . cm

First digit (known)First digit (known) = 2 = 2 2.?? cm2.?? cm

Second digit (known)Second digit (known) = 0.7 = 0.7 2.7? cm2.7? cm

Third digit (estimated) between 0.05- 0.07Third digit (estimated) between 0.05- 0.07

Length reportedLength reported == 2.75 cm 2.75 cm

oror 2.74 cm 2.74 cm

oror 2.76 cm2.76 cm

54. Known + Estimated Digits54. Known + Estimated Digits

In 2.76 cm…In 2.76 cm…

• Known digitsKnown digits 2 andand 7 are 100% certainare 100% certain

• The third digit 6 is estimated (uncertain)The third digit 6 is estimated (uncertain)

• In the reported length, all three digits In the reported length, all three digits (2.76 cm) are significant including the (2.76 cm) are significant including the estimated oneestimated one

#23 .Learning Check#23 .Learning Check

. l8. . . . I . . . . I9. . . .I . . . . I10. . cm

What is the length of the line?What is the length of the line?

1) 9.6 cm 1) 9.6 cm

2) 9.62 cm 2) 9.62 cm

3) 9.63 cm3) 9.63 cm

How does your answer compare with your How does your answer compare with your

neighbor’s answer? Why or why not?neighbor’s answer? Why or why not?

55.Zero as a Measured Number55.Zero as a Measured Number

. l3. . . . I . . . . I4 . . . . I . . . . I5. . cm

What is the length of the line?What is the length of the line?

First digitFirst digit 5.?? cm5.?? cm

Second digitSecond digit 55.0? cm.0? cm

Last (estimated) digit isLast (estimated) digit is 5.05.00 cm0 cm

56. Solving Scientific Problems

Read Draw Given Find

Equation Solution Final Answer

56.Problem Solving Steps1. Read the

problems several times.(READ)

2. Make illustration to describe the problem.(DRAW)

3. Write the given data.(GIVEN)

4. Determine the unknown .(FIND)

5. Write the appropriate equation that connects the given data to the unknown.(EQUATION)

6. Substitute the given into the equation to solve the unknowns. (SOLUTION)

7. Enclose your final answer with a box.(FINAL ANSWER )

57.Unit Conversion Example: Is he speeding ?

On the garden state parkway of New Jersey, a car is traveling at a speed of 38.0 m/s. Is the driver exceeding the speed limit?

Put 1’s using unit conversion relations, as many times as necessary.

Multiply or divide numbers and units. Begin with 38.0 m/s = (38.0 m/s) 1 Since 1 mile = 1609 m, so we have 1 = 1 mile/1609 m

Then

Finally

smiles

mile

m

mile

s

m/1036.2

1600

0.38)

1609

1()0.38( 2

September 4, 2008

hrmilehr

mile

hr

mile

miles

s

mile

s

mile

/0.8560601036.21

min60

min601036.2

min601036.2

min1

601036.21036.2

22

222

DENSITYDENSITY - an important - an important and useful physical propertyand useful physical property

Mercury

13.6 g/cm13.6 g/cm33 21.5 g/cm21.5 g/cm33

Aluminum

2.7 g/cm2.7 g/cm33

Platinum

58. Problem58. Problem A piece of copper has a A piece of copper has a mass of 57.54 g. It is 9.36 cm long, mass of 57.54 g. It is 9.36 cm long, 7.23 cm wide, and 0.95 mm thick. 7.23 cm wide, and 0.95 mm thick. Calculate density (g/cmCalculate density (g/cm33).).

StrategyStrategy1. Get dimensions in common units.1. Get dimensions in common units.

2.2. Calculate volume in cubic Calculate volume in cubic centimeters.centimeters.

3. Calculate the density.3. Calculate the density.

SOLUTIONSOLUTION1. Get dimensions in common units.1. Get dimensions in common units.

2.2. Calculate volume in cubic Calculate volume in cubic centimeters.centimeters.

3. Calculate the density.3. Calculate the density.

(9.36 cm)(7.23 cm)(0.095 cm) = 6.4 cm(9.36 cm)(7.23 cm)(0.095 cm) = 6.4 cm33

Note only 2 significant figures in the answer!Note only 2 significant figures in the answer!

59. PROBLEM: Mercury (Hg) has a density 59. PROBLEM: Mercury (Hg) has a density of 13.6 g/cmof 13.6 g/cm33. What is the mass of 95 mL . What is the mass of 95 mL of Hg in grams? In pounds?of Hg in grams? In pounds?

59. PROBLEM: Mercury (Hg) has a density 59. PROBLEM: Mercury (Hg) has a density of 13.6 g/cmof 13.6 g/cm33. What is the mass of 95 mL . What is the mass of 95 mL of Hg in grams? In pounds?of Hg in grams? In pounds?

Solve the problem usingSolve the problem using DIMENSIONAL DIMENSIONAL ANALYSIS.ANALYSIS.

PROBLEM: Mercury (Hg) has a density of PROBLEM: Mercury (Hg) has a density of 13.6 g/cm13.6 g/cm33. What is the mass of 95 mL of . What is the mass of 95 mL of Hg?Hg?


StrategyStrategy1.1. Use density to calc. mass (g) from Use density to calc. mass (g) from volume.volume.2.2. Convert mass (g) to mass (lb)Convert mass (g) to mass (lb)

Need to know conversion factorNeed to know conversion factor= 454 g / 1 lb= 454 g / 1 lb

First, note thatFirst, note that 1 cm1 cm33 = 1 mL = 1 mL



1.1. Convert volume to massConvert volume to mass

2.2. Convert mass (g) to mass (lb)Convert mass (g) to mass (lb)


Osmium is a very dense metal. What is its Osmium is a very dense metal. What is its

density in g/cmdensity in g/cm3 3 if 50.00 g of the metal if 50.00 g of the metal occupiesoccupies

a volume of 2.22cma volume of 2.22cm33??

1) 2.25 g/cm1) 2.25 g/cm33

2)2) 22.5 g/cm22.5 g/cm33

3)3) 111 g/cm111 g/cm33

Solution

2) Placing the mass and volume of the 2) Placing the mass and volume of the osmium metal into the density setup, we osmium metal into the density setup, we obtainobtain

D = D = massmass = = 50.00 g 50.00 g = = volumevolume 2.22 cm2.22 cm33

= 22.522522 g/cm= 22.522522 g/cm3 3 == 22.5 g/cm22.5 g/cm33

#25.Volume Displacement#25.Volume Displacement

A solid displaces a matching volume of A solid displaces a matching volume of water when the solid is placed in water.water when the solid is placed in water.

33 mL33 mL25 mL 25 mL


What is the density (g/cmWhat is the density (g/cm33) of 48 g of a metal ) of 48 g of a metal if the metal raises the level of water in a if the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL? graduated cylinder from 25 mL to 33 mL?

1) 0.2 g/ cm1) 0.2 g/ cm33 2) 6 g/m 2) 6 g/m33 3) 252 3) 252 g/cmg/cm33

33 mL33 mL 25 mL25 mL

#27. Learning CheckLearning Check

Which diagram represents the liquid layers in Which diagram represents the liquid layers in the cylinder?the cylinder?

(K) Karo syrup (1.4 g/mL), (V) vegetable oil (K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL)(0.91 g/mL,) (W) water (1.0 g/mL)

1)1) 2) 2) 3) 3)

K

K

W

W

W

V

V

V

K

SolutionSolution

(K) Karo syrup (1.4 g/mL), (V) vegetable (K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL)oil (0.91 g/mL,) (W) water (1.0 g/mL)

1)1)

K

W

V


The density of octane, a component The density of octane, a component of gasoline, is 0.702 g/mL. What is of gasoline, is 0.702 g/mL. What is the mass, in kg, of 875 mL of octane?the mass, in kg, of 875 mL of octane?

1) 0.614 kg1) 0.614 kg

2) 614 kg2) 614 kg

3) 1.25 kg3) 1.25 kg


If blood has a density of 1.05 g/mL, If blood has a density of 1.05 g/mL, how many liters of blood are donated how many liters of blood are donated if 575 g of blood are given?if 575 g of blood are given?

1) 1) 0.548 L0.548 L

2) 2) 1.25 L1.25 L

3) 3) 1.83 L1.83 L

#30.Learning CheckLearning Check

A group of students collected 125 empty A group of students collected 125 empty aluminum cans to take to the recycling aluminum cans to take to the recycling center. If 21 cans make 1.0 pound of center. If 21 cans make 1.0 pound of aluminum, how many liters of aluminum aluminum, how many liters of aluminum (D=2.70 g/cm(D=2.70 g/cm33) are obtained from the cans?) are obtained from the cans?

1) 1.0 L1) 1.0 L 2) 2.0 L2) 2.0 L 3) 4.0 L3) 4.0 L

60. Scientific Method1.1. State the problem clearly.State the problem clearly.2.2. Gather information.Gather information.3.3. Form a hypothesis.Form a hypothesis.4.4. Test the hypothesis.Test the hypothesis.5.5. Evaluate the data to form a Evaluate the data to form a

conclusion.conclusion. If the conclusion is valid, then it If the conclusion is valid, then it becomes a becomes a theorytheory. If the theory is . If the theory is found to be true over along period of found to be true over along period of time (usually 20+ years) with no time (usually 20+ years) with no counter examples, it may be considered counter examples, it may be considered a a lawlaw..

6. Share the results.6. Share the results.

Vector vs. Scalar Review

All physical quantities encountered in this text will be either a scalar or a vector

A vector quantity has both magnitude (value + unit) and direction A scalar is completely specified by only a magnitude (value + unit)

September 4, 2008

A library is located 0.5 mi from you. Can you point where exactly it is?

You also need to know the direction in which you should walk to the library!

61. Vector and Scalar Quantities

Vectors Displacement Velocity (magnitude

and direction!) Acceleration Force Momentum

Scalars: Distance Speed (magnitude of

velocity) Temperature Mass Energy Time

To describe a vector we need more information than to describe a scalar! Therefore vectors are more complex!

Important Notation

To describe vectors we will use: The bold font: Vector A is A Or an arrow above the vector: In the pictures, we will always

show vectors as arrows Arrows point the direction To describe the magnitude of a

vector we will use absolute value sign: or just A,

Magnitude is always positive, the magnitude of a vector is equal to the length of a vector.

A

A

62.Properties of Vectors Equality of Two Vectors

Two vectors are equal if they have the same magnitude and the same direction

Movement of vectors in a diagram Any vector can be moved parallel

to itself without being affected

A B

Negative Vectors Two vectors are negative if they have the same

magnitude but are 180° apart (opposite directions) ; 0 A B A A

63.Adding Vectors When adding vectors, their directions

must be taken into account Units must be the same Geometric Methods

Use scale drawings Algebraic Methods

More convenient

64.Adding Vectors Geometrically (Triangle Method)

Draw the first vector with the appropriate length and in the direction specified, with respect to a coordinate system

Draw the next vector with the appropriate length and in the direction specified, with respect to a coordinate system whose origin is the end of vector and parallel to the coordinate system used for : “tip-to-tail”.

The resultant is drawn from the origin of to the end of the last vector

A

B

A

BA

A

B

A

A

B

65. Adding Vectors Graphically When you have

many vectors, just keep repeating the process until all are included

The resultant is still drawn from the origin of the first vector to the end of the last vector

BA

BA

September 4, 2008

CBA

66.Adding Vectors Geometrically (Polygon Method)

Draw the first vector with the appropriate length and in the direction specified, with respect to a coordinate system

Draw the next vector with the appropriate length and in the direction specified, with respect to the same coordinate system

Draw a parallelogram The resultant is drawn as a

diagonal from the originABBA

September 4, 2008

A

B

A

BA

B

67.Vector SubtractionSpecial case of vector

addition Add the negative of the

subtracted vector

Continue with standard vector addition procedure

B

A B A B

A

B

BA

Describing Vectors Algebraically

Vectors: Described by the number, units and direction!

Vectors: Can be described by their magnitude and direction. For example: Your displacement is 1.5 m at an angle of 250.

Can be described by components? For example: your displacement is 1.36 m in the positive x direction and 0.634 m in the positive y direction.

68.Components of a Vector A component is a part It is useful to use

rectangular components These are the projections of the vector along the x- and y-axes

cosa

cosa

sina

68.Components of a VectorThe x-component of a vector is the projection along the x-axis

The y-component of a vector is the projection along the y-axis

Then, yx AAA

x y A A A

cos xA

A cosxA A

sinyA

A sinyA A

69. Components of a Vector

The previous equations are valid only if θ is measured with respect to the x-axis

The components can be positive or negative and will have the same units as the original vector

θ

θ=0, Ax=A>0, Ay=0

θ=45°, Ax=Acos45°>0, Ay=Asin45°>0 θ=90°, Ax=0, Ay=A>0

θ=135°, Ax=Acos135°<0, Ay=Asin135°>0

θ=180°, Ax=-A<0, Ay=0

θ=225°, Ax=Acos225°<0, Ay=Asin225°<0 θ=270°, Ax=0, Ay=-A<0

θ=315°, Ax=Acos315°<0, Ay=Asin315°<0

ax > 0ay > 0

ax < 0ay > 0

ax < 0ay < 0

ax > 0ay < 0

70. More About Components The components are the legs

of the right triangle whose hypotenuse is A

September 4, 2008

2 2 1tan yx y

x

AA A A and

A

x

y

x

y

yx

y

x

A

A

A

A

AAA

AA

AA

1

22

tanor tan

)sin(

)cos(

Or,

Unit Vectors Component of a vector is still

vectors Vectors have units (i.e. m/s)

Unit vectors used to specify direction

Unit vectors have a magnitude of 1

Then

x y A A A

zk ˆxi ˆ yj ˆ

y

x

z

ij

k

yx AAA

jAiAA yxˆˆ

Magnitude + Sign Unit vector

Adding Vectors Algebraically Consider two vectors

Then

If so

September 4, 2008

x y A A A jBAiBABAC yyxx

ˆ)(ˆ)(

jBAiBA

jBiBjAiABA

yyxx

yxyx

ˆ)(ˆ)(

)ˆˆ()ˆˆ(

jBiBB yxˆˆ

jAiAA yxˆˆ

xxx BAC yyy BAC

September 4, 2008

Example : Operations with Vectors

Vector A is described algebraically as (-3, 5), while

vector B is (4, -2). Find the value of magnitude and

direction of the sum (C) of the vectors A and B.

jijiBAC ˆ3ˆ1ˆ)25(ˆ)43(

jiB ˆ2ˆ4

jiA ˆ5ˆ3

1xC 3yC

16.3)31()( 2/1222/122 yx CCC

56.713tantan 11

x

y

C

C

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