Welcome to the Welcome to the World of World of Physical Physical ScienceScience

Types of Observations and Types of Observations and MeasurementsMeasurements

• We makeWe make QUALITATIVEQUALITATIVE observations of reactions — observations of reactions — changes in color and physical changes in color and physical state.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 measurementSI measurement• Le Système international Le Système international

d'unitésd'unités • The only countries that have not The only countries that have not

officiallyofficially adopted SI are Liberia adopted SI are Liberia (in western Africa) and Myanmar (in western Africa) and Myanmar (a.k.a. Burma, in SE Asia), but (a.k.a. Burma, in SE Asia), but now these are reportedly using now these are reportedly using metric regularlymetric regularly

• Metrication is a process that Metrication is a process that does not happen all at once, but does not happen all at once, but is rather a process that happens is rather a process that happens over time. 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 only country significantly holding outcountry significantly holding out.. The U.S. officially adopted SI in The U.S. officially adopted SI in 1866.1866.

Information from U.S. Metric Association

Physical Science In ActionPhysical Science In Action

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

When we measure, we use a measuring tool to When we measure, we use a measuring tool to compare some dimension of an object to a standard.compare some dimension of an object to a 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?

Stating a MeasurementStating 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 measurement!The number should also be as precise as the measurement!

UNITS OF UNITS OF MEASUREMENTMEASUREMENT

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

Length Length

MassMass

VolumeVolume

TimeTime

TemperatureTemperature

Meter, mMeter, m

Kilogram, kgKilogram, kg

Seconds, sSeconds, s

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

Liter, LLiter, L

Mass vs. WeightMass vs. Weight

• Mass: Amount Mass: Amount of Matter (grams, of 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?

Some Tools for 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

Learning Check

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

____ 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

Learning CheckLearning Check

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

A. length A. length

B. volume B. volume

C. weightC. weight

D. temperatureD. temperature

Metric PrefixesMetric 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)

Metric PrefixesMetric Prefixes

Metric PrefixesMetric Prefixes

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

Learning Check

Units of Units of LengthLength

• ? 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

Learning Check

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) kilometers c) kilometers

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

Conversion FactorsConversion Factors

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

Example: 1 in. = 2.54 cm

Factors: 1 in. and 2.54 cm

2.54 cm 1 in.

Learning Check

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

How many minutes are in 2.5 hours?

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!

Steps to Problem SolvingSteps to Problem Solving1. Write down the given amount. Don’t forget the units!2. Multiply by a fraction.3. Use the fraction as a conversion factor. Determine if

the top or the bottom should be the same unit as the given so that it will cancel.

4. Put a unit on the opposite side that will be the new unit. If you don’t know a conversion between those units directly, use one that you do know that is a step toward the one you want at the end.

5. Insert the numbers on the conversion so that the top and the bottom amounts are EQUAL, but in different units.

6. Multiply and divide the units (Cancel).7. If the units are not the ones you want for your

answer, make more conversions until you reach that point.

8. Multiply and divide the numbers. Don’t forget “Please Excuse My Dear Aunt Sally”! (order of operations)

Sample Problem

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

7.25 dollars 4 quarters7.25 dollars 4 quarters

1 dollar1 dollar X = 29 quarters= 29 quarters

Learning Check

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

a) a) 2440 cm2440 cm

b)b) 244 cm244 cm

c)c) 24.4 cm24.4 cm

Solution

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

b)b) 244 cm244 cm

2.44 m x 2.44 m x 100 cm 100 cm = 244 cm= 244 cm

1 m

Learning Check

How many seconds are in 1.4 days?

Unit plan: days hr min seconds

1.4 days x 24 hr x ?? 1 day

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 sec 60 sec

24 hr 1 hr 1 min24 hr 1 hr 1 min

English and Metric English and Metric ConversionsConversions

• If 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 these and use these conversions:conversions:

–Mass: 454 grams = 1 poundMass: 454 grams = 1 pound

–Length: 2.54 cm = 1 inchLength: 2.54 cm = 1 inch

–Volume: 0.946 L = 1 quartVolume: 0.946 L = 1 quart

Learning CheckLearning Check

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

Unit plan: L qt gallon

Equalities: 1 quart = 0.946 L

1 gallon = 4 quarts

Your Setup:

Equalities

State the same measurement in two different State the same measurement in two different unitsunits

lengthlength

10.0 in.10.0 in.

25.4 cm25.4 cm

Steps to Problem SolvingSteps to Problem Solving

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

desired unitdesired 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

Dealing with Two Units – Honors Dealing with Two Units – Honors OnlyOnly

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

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

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

• Best way: Square or cube the ENITRE Best way: Square or cube the ENITRE conversion factorconversion 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

Learning CheckLearning Check

• A Nalgene water A Nalgene water bottle holds 1000 bottle holds 1000 cmcm33 of dihydrogen of 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.

Always estimate ONE place past the smallest mark!Always estimate ONE place past the smallest mark!

What is Density???What is Density???

• The Amount of Matter in a Given Space

• Mass per Unit Volume

• Units: solids g/cm3; liquids g/mL;

gas g/L

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

Density mass (g)volume (cm3)

Density mass (g)volume (cm3)

Mercury

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

Aluminum

2.7 g/cm2.7 g/cm33

Platinum

ProblemProblem 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).).

Density mass (g)volume (cm3)

Density mass (g)volume (cm3)

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

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

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

SOLUTIONSOLUTION

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

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

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

0.95 mm • 1cm

10 mm = 0.095 cm

57.54 g

6.4 cm3 = 9.0 g / cm3

(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!

PROBLEM: Mercury (Hg) has a density 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?

PROBLEM: Mercury (Hg) has a density 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?

StrategyStrategy

1.1. 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

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 Hg?. What is the mass of 95 mL of Hg?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 Hg?. What is the mass of 95 mL of Hg?

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

1.1. Convert volume to massConvert volume to mass

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

95 cm3 • 13.6 g

cm3 = 1.3 x 103 g

1.3 x 103 g • 1 lb

454 g = 2.8 lb

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

Learning CheckLearning Check

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 occupiesif 50.00 g of the metal occupies

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

D = D = massmass = = 50.00 g 50.00 g = = volumevolume2.22 cm2.22 cm33

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

Volume DisplacementVolume 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

Learning CheckLearning Check

What is the density (g/cmWhat is the density (g/cm33) of 48 g of a metal if ) of 48 g of a metal if the metal raises the level of water in a graduated the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL? 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 g/cm3) 252 g/cm33

33 mL33 mL

25 mL25 mL

Learning CheckLearning Check

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

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

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

K

K

W

W

W

V

V

V

K

Learning CheckLearning Check

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

Learning CheckLearning Check

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

Learning CheckLearning Check

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

Scientific MethodScientific Method

1.1. State the problem clearly.State the problem clearly.2.2. Gather information (librarey research)Gather information (librarey research)3.3. Form a _______________.Form a _______________.4.4. Test the hypothesis (usually perform an Test the hypothesis (usually perform an

experimentexperiment5.5. Evaluate the data to form a conclusion.Evaluate the data to form a conclusion.

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

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

What is Scientific Notation?What is Scientific Notation?

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

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

Scientific notation consists Scientific notation consists of two parts: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

To change standard form To change standard form to scientific notation…to scientific notation…

• Place the decimal point so that there is Place the decimal point so that there is one non-zero digit to the left of the 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 1, If the original number was less than 1, then the exponent is negative. If the then the exponent is negative. If the original number was greater than 1, original number was greater than 1, then the exponent is positive.then the exponent is positive.

ExamplesExamples

• Given: 289,800,000Given: 289,800,000

• Use: 2.898 (moved 8 places)Use: 2.898 (moved 8 places)

• Answer:Answer: 2.898 x 102.898 x 1088

• Given: 0.000567Given: 0.000567

• Use: 5.67 (moved 4 places)Use: 5.67 (moved 4 places)

• Answer:Answer: 5.67 x 105.67 x 10-4-4

To change scientific To change scientific notation to standard notation to standard

form…form…• Simply move the decimal point to Simply move the decimal point to

the right for positive exponent 10. the right for positive exponent 10.

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

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

ExampleExample

• Given: 5.093 x 10Given: 5.093 x 1066

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

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

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

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