Copyright © 2011 Pearson Education, Inc. Approaches to Problem Solving 2A Discussion Paragraph 1 web 87. S. American Adventure 88. Polar Ice Melting 1

Copyright © 2011 Pearson Education, Inc.

Approaches to Problem Solving

2A Discussion Paragraph

1 web 87. S. American Adventure88. Polar Ice Melting

1 world89. Are the units clear90. Units on the Highway91. False Advertising

Copyright © 2011 Pearson Education, Inc. Slide 2-3

Unit 2B

Standardized Units: More Problem-Solving Power

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Standardized Unit Systems

The International Metric System (or SI)

Wide international use

U.S. Customary System (USCS) (or English system)

Used in the United States

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Units of length were based on individual body measurements.

A foot was once the length of the measurer’s foot. An inch was the thumb-width of the measurer. A mile was one thousand paces.

There are three distinct sets of units used to measure weight.1. Jewelers used troy measures of weight.2. Pharmacists used apothecary measures of weight.3. Other commerce was conducted with avoirdupois

measures of weight. The basic unit of volume is the cubic inch (in.3).

Dry and liquid measures differ.

U.S. Customary System

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2-BThe Kentucky DerbyCN 1

1. The length of the Kentucky Derby horse race is 10 furlongs. How long is the race in miles?


2-B20,000 Leagues Under the SeaCN 2

2. In Jules Verne’s novel 20,000 Leagues Under the Sea (published in 1870), does the title refer to an ocean depth?

How do you know?


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1 km = 0.6214 mi (1 km)2 = (0.6214 mi)2

Metric-USCS Conversions

How many square miles are in a square kilometer?

1 km2 ≈ 0.3861 mi2

2-BClass Notes (4)You try

4. A speed boat has a top speed of 46 knots (nautical miles per hour). What is this speed in miles per hour?


2-BClass Notes (5)You try

5. How many cords of wood could you fit in a room that is 4 yards long, 4 yards wide, and 2 yards high?


2-B


International Metric System

The metric system was designed to

1. replace many customary units with a few basic units.

2. simplify conversions through the use of a decimal (base 10) system.

The following are basic metric units: meter (m) for length kilogram (kg) for mass second (s) for time liter (L) for volume * Historical Note

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Base Systems

* Historical Note p.99

Base 10 system (money) Base 60 system (time)


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Metric Conversions

Moving between metric units requires shifting the decimal placeone to the right when going to the next smaller unit and one to theleft when going to the next larger unit.

(Example: 5.23 cm = 52.3 mm)

2-BClass Notes (7-9)You try

7. A meter is __________times as large as a millimeter.

8. A kilometer is _______ times as large as a micrometer.

9. A square meter is _________ times as large as a square centimeter.


2-BGas Price per LiterCN 4

A gas station in Canada sells gasoline for CAD 1.10 per liter. (CAD is an abbreviation for Canadian dollars.)

Conversion rate for liters to gallons. ________

4. What is the price in dollars per gallon?


2-BSquare Kilometers to Square MilesCN 5a-h

5 a. How many square km are in one square mile?


2-BConvert the following quantities 5b-h

b. 22 kilograms to pounds __________ c. 16 quarts to liters ________ d. 2 square kilometers t square miles ______ e. 55 miles per hour to kilometers per hour ____ f. 18 meters per second to miles per hour ____ g. 160 centimeters to inches _______ h. 120 kilometers per hour to miles per hour ___


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Temperature Units

Three temperature scales are commonly used today.

A temperature of 0 K is the coldest possible temperature, known as absolute zero.

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Temperature Conversions

The conversions are given in both words and with formulas in which C, F, and K are Celsius, Fahrenheit, and Kelvin temperatures, respectively.

C = K 273.15Subtract 273.15Kelvin to Celsius

K = C + 273.15Add 273.15.Celsius to Kelvin

Subtract 32. Then divide by 1.8

Fahrenheit to Celsius

F = 1.8C + 32Multiply by 1.8. Then add 32.

Celsius to Fahrenheit

Conversion Formula

Conversion in Words

To Convert from

2-BHuman Body TemperatureCN 6a-h

6. Average human body temp is 98.6 degrees Fahrenheit.

a. What is it in Celsius and Kelvin?


2-BConvert to other temperature6b-h

b. 45 degrees F _______ C c. 20 degrees C _______ F d. -15 degrees C _______ F e. -8 degrees C _______ F f. 70 degrees F _______ C g. 20 degrees F _______ F h. 15 degrees C _______ F


2-B


Units of Energy and Power

Energy is what makes matter move or heat up. International metric unit is the joule

Power is the rate at which energy is used. International metric unit is the watt

A kilowatt-hour is a unit of energy.

1 kilowatt-hour = 3.6 million joules

s

joule1 watt1

2-BRunning PowerCN 7

7. Assume that running consumes 100 Calories per mile.

If you run 10 minute miles, what is your average power output, in watts, during a 1 hour run?


2-B


Operating Cost of a Light Bulb

A utility company charges 12.5¢ per kilowatt-hour of electricity. How much does it cost to keep a 75-watt light bulb on for a week?

One watt = 1 joule/sec, so a 75-watt bulb uses 75 joules/sec. Find the number of joules used in a week:

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Convert this result to kilowatt-hours:

Now find the total cost:

Operating Cost of a Light Bulb

2-BCalculateCN 8a-b Calculate both energy and power use in the next

two questions: Total energy use in joules Your average power use in watts

8a. In May you used 900 kilowatt-hours of energy for electricity.

8b. In October you used 1050 kilowatt0hours of energy for electricity.


2-B

FYI Practical Matters p.105

Save Money and Save the Earth (this is a great read)

Light vs. Heat


2-B


Density describes compactness or crowding.

Material density is given in units of mass per unit volume.

e.g., grams per cubic centimeter (g/cm3) Population density is given by the number of

people per unit area. e.g., people per square mile (people/mi2)

Information density is given in units of mass per unit volume.

e.g., gigabytes per square inch (GB/in.2)

Units of Density and Concentration

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The concentration of an air pollutant is often measured by the number of molecules of the pollutant per million molecules of air.

e.g., parts per million (ppm)

Blood alcohol content (BAC) describes the concentration of alcohol in a person’s body.

e.g., grams of alcohol per 100 milliliters of blood

Concentration describes the amount of one substance mixed with another.

Units of Density and Concentration

2-BNew York CityCN 9a-b

9. Manhattan Island has a population of about 1.5 million people living in an area oa bout 57 square kilometers.

a. What is its population density?

b. If there were no high rise apartments, how much space would be available per person?


2-BBlood Alcohol ContentCN 10a-b

A typical glass of wine contains about 20 grams of alcohol. Consider a 110 lb. woman, with approximately 4 liters (4000 milliliters) of blood, who drinks two glasses of wine.

10a. If all alcohol was absorbed immediately into her bloodstream, what would her blood alcohol content be?

Is it safe for her to drive at this time? ExplainCopyright © 2011 Pearson Education, Inc. Slide 2-34

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Con’t

Again assume the alcohol is absorbed immediately, but now assume that her body eliminates the alcohol (through metabolism) at a rate of 10 grams per hour.

10b. What is her blood alcohol content 3 hours after drinking the wine?

Is it safe for her to drive at this time? Explain.


2-BHomework 2B

DP: 2A CN: 1 -10 QQ: 1-10 P.108:1-18 1 web

91. Everyday Metric 92. Energy 93. Density and Concentration 94. Utility Bill

1 world 95. Unit Conversions 96. Currency Conversions


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Copyright © 2011 Pearson Education, Inc. Approaches to Problem Solving 2A Discussion Paragraph 1 web 87. S. American Adventure 88. Polar Ice Melting 1