Copyright © 2011 Pearson Education, Inc. Approaches to Problem Solving

Copyright © 2011 Pearson Education, Inc. Slide 2-3 Unit 2B Standardized Units: More Problem-Solving Power

2-B Copyright © 2011 Pearson Education, Inc. Slide 2-4 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

2-B Copyright © 2011 Pearson Education, Inc. Slide 2-5 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

2-B Copyright © 2011 Pearson Education, Inc. Slide 2-6 U.S. Customary System

2-B Class Notes (1-2) Ex 2: 20,000 Leagues Under the Sea 1. In Jules Verne’s novel 20,000 Leagues Under the Sea (published in 1870), does the title refer to an ocean depth? 2. How do you know? Copyright © 2011 Pearson Education, Inc. Slide 2-7

2-B Copyright © 2011 Pearson Education, Inc. Slide 2-8 U.S. Customary System

2-B Copyright © 2011 Pearson Education, Inc. Slide 2-9 U.S. Customary System

2-B Class Notes (3) Ex 1: The Kentucky Derby 3. The length of the Kentucky Derby horse race is 10 furlongs. How long is the race in miles? Copyright © 2011 Pearson Education, Inc. Slide 2-10

2-B Copyright © 2011 Pearson Education, Inc. Slide km = mi (1 km) 2 = ( mi) 2 Metric-USCS Conversions How many square miles are in a square kilometer? 1 km 2 ≈ mi 2

2-B Class 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? Copyright © 2011 Pearson Education, Inc. Slide 2-12

2-B Class 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? Copyright © 2011 Pearson Education, Inc. Slide 2-13

2-B Copyright © 2011 Pearson Education, Inc. Slide 2-14 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

2-B Base Systems * Historical Note p.99 Base 10 system (money) Base 60 system (time) Copyright © 2011 Pearson Education, Inc. Slide 2-15

2-B Copyright © 2011 Pearson Education, Inc. Slide 2-16 Metric Conversions Moving between metric units requires shifting the decimal place one to the right when going to the next smaller unit and one to the left when going to the next larger unit. (Example: 5.23 cm = 52.3 mm)

2-B Class 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. Copyright © 2011 Pearson Education, Inc. Slide 2-17

2-B Class Notes (10-12) Ex 4: Gas Price per Liter 10.*what is the currency exchange rate? A gas station in Canada sells gasoline for CAD 1.10 per liter. (CAD is an abbreviation for Canadian dollars.) 11. Conversion rate for liters to gallons. 12. What is the price in dollars per gallon? Copyright © 2011 Pearson Education, Inc. Slide 2-18

2-B Class Notes (13-19) Convert the following quantities (group) kilograms to pounds __________ quarts to liters ________ square kilometers t square miles ______ miles per hour to kilometers per hour ____ meters per second to miles per hour ____ centimeters to inches _______ kilometers per hour to miles per hour ___ Copyright © 2011 Pearson Education, Inc. Slide 2-19

2-B Copyright © 2011 Pearson Education, Inc. Slide 2-20 Temperature Units Three temperature scales are commonly used today. A temperature of 0 K is the coldest possible temperature, known as absolute zero.

2-B Copyright © 2011 Pearson Education, Inc. Slide 2-21 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  Subtract Kelvin to Celsius K = C Add 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-B Class Notes (20-26) Convert to other temperature degrees F_______ C degrees C_______ F degrees C_______ F degrees C_______ F degrees F_______ C degrees F_______ F degrees C_______ F Copyright © 2011 Pearson Education, Inc. Slide 2-22

2-B Copyright © 2011 Pearson Education, Inc. Slide 2-23 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

2-B Class Notes (26) Running Power 26. 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? Copyright © 2011 Pearson Education, Inc. Slide 2-24

2-B Copyright © 2011 Pearson Education, Inc. Slide 2-25 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:

2-B Copyright © 2011 Pearson Education, Inc. Slide 2-26 Convert this result to kilowatt-hours: Now find the total cost: Operating Cost of a Light Bulb

2-B Class Notes (27-28) Calculate Calculate both energy and power use in the next two questions: Total energy use in joules Your average power use in watts 27. In May you used 900 kilowatt-hours of energy for electricity. 28. In October you used 1050 kilowatt0hours of energy for electricity. Copyright © 2011 Pearson Education, Inc. Slide 2-27

2-B FYI Practical Matters p.105 Save Money and Save the Earth (this is a great read) Light vs. Heat Copyright © 2011 Pearson Education, Inc. Slide 2-28

2-B Copyright © 2011 Pearson Education, Inc. Slide 2-29 Density describes compactness or crowding. Material density is given in units of mass per unit volume. e.g., grams per cubic centimeter (g/cm 3 ) Population density is given by the number of people per unit area. e.g., people per square mile (people/mi 2 ) 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

2-B Copyright © 2011 Pearson Education, Inc. Slide 2-30 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-B Class Notes (29) Blood Alcohol Content 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. 29. 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? Explain Copyright © 2011 Pearson Education, Inc. Slide 2-31

2-B Class Notes (30) 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. 30. What is her blood alcohol content 3 hours after drinking the wine? Is it safe for her to drive at this time? Explain. Copyright © 2011 Pearson Education, Inc. Slide 2-32