Ch. 2 – Measuring and Calculating Problem Solving Techniques #1 – Identify the known facts. #2 – Define the answer required (find the question) Based on careful reading of the problem. Understand all symbols, words, and units. Read the problem a second time more carefully. Write down all pieces of information given. Write down the unknown to be determined. Problem Solving Techniques #3 – Develop possible solutions. Determine relevant vs. irrelevant info. Write down the possible ways to answer the question. #4 – Analyze solutions and determine the correct one. Problem Solving Techniques #5 – Develop the individual steps to arrive at the answer. Helps you to recognize algorithms over time. Algorithm – a pattern for solving a particular type of problem. #6 - Solve the problem. Problem Solving Techniques Final Step: #7 – Evaluate the results. Is the answer reasonable? Check: what unit do you want? Is it the unit that you have? magnitude – size of answer too big or small? units – Let’s Try a Problem 15 members of a school soccer team want to get t-shirts imprinted with the school name. Each shirt costs $9.00 and each imprint costs $2.00. To raise money for the shirst, the team members decide to sell candy bars at $.50 each, of which 20 cents is profit. How many bars must each team member sell? Apply the 7 steps. Section 2.2 – Numerical Problem Solving Quantitative – describing a property using a measurement of a number of units 5g 0.002 s 1.2 in. 400 m 8 apples 30 days Qualitative – describing a property without measurements Dark Cold - heavy - humid - wet - turquoise 2.2 - THE INTERNATIONAL SYSTEM (SI) System of measurement used by all scientists all over the Earth Uses Base Units (p 29) Modifies bases using Prefixes (p29) Prefixes are equal to different quantities Indicates that a unit should be multiplied by the equivalent number 2.2 - THE INTERNATIONAL SYSTEM (SI) http://www.moe.gov.sg/edumall/tl/digital_resources/physics/images/SI_base_quantities.jpg 2.2 - THE INTERNATIONAL SYSTEM (SI) http://itl.chem.ufl.edu/2045_s00/matter/TB01_005.GIF Practice Which is bigger? kilogram or megagram? centimeter or millimeter? What is the name of the quantity using prefixes and base units? 1000 L 0.001 s -- 1,000,000 cd -- 0.000 000 001 mol 2.2 - MASS AND WEIGHT Mass – measure of the quantity of matter Doesn’t change regardless of location on Earth Kilogram – SI standard mass unit Balance – used to determine the mass of an object by comparing an unknown mass to a known mass “Massing” – using a balance to determine the mass of an object 2.2 - MASS AND WEIGHT Weight – measure of the force of gravity between two objects Changes as gravity changes with location on Earth Higher altitude less gravity – lighter weight Lower altitude greater gravity – heavier weight Moon less gravity – weigh less 2.2 - Length, Time and Temperature Length – the distance of a straight line between two points unit = meter (m) tool = ruler or measuring tape Time – 1/86,400 of a day unit = second tool = clock (s) Temperature – the avg. KE of the particles in an object unit = Kelvin (K) tool = thermometer **** 2.2 – Temperature and Celsius Celsius (degree C) – based on freezing and boiling point of water Freezing point of water = 0 C Boiling point of water = 100 C As something is heated, temp. increases - indicates that KE is increasing 2.2 - ACCURACY AND PRECISION Accuracy – how close a measurement is to the accepted value 42.3 m = accepted 42.2 m = accurate 23 m = inaccurate 100m = inaccurate Precision – how close a set of measurements are to each other 22.6 m, 22.7 m, 22.3m – precise 42.3 m, 42.1m, 42.4m – precise 30 m, 82m, 12 m – not precise 2.2 - PERCENT ERROR Used to compare your value to an accepted value Evaluates the accuracy of your measurement I your measurement – accepted I %Error = ------------------------------------------accepted 2.2 - SIGNIFICANT DIGITS Indicates exactness of a measurement Rules Digits other than zero are always significant Final zeros after a decimal point are always significant Zeros between two sig. dig are significant Zeros used solely for spacing the decimal point (placeholders) are not significant. 2.2 - PERCENT ERROR - Sample problem – text p35 “A student determines the atomic mass of Aluminum to be 28.9 amu. If the accepted value is 27.0 amu, what is the percent error?” I 28.9 – 27.0 I ------------------- x 100% = 7.0% error 27.0 2.2 - SIGNIFICANT DIGITS Counting – inifinite significant digits. Examples: $842.30 – 42 students – 39.7 s – 0.0076 g – 300 m – 230,000.0 – 5 sig.digs inifinite sig.digs 3 sig.digs 2 sig.digs 1 sig.dig 7 sig.digs 2.2 - DERIVED UNITS Combinations of units to make measurements EXAMPLES: Speed – m/s Volume – cm3 Density = m/V = mass/volume unit -- g/ cm3 Changes with temperature because volume changes with temperature. 2.2 - DENSITY A standard value that can be used to calculate mass and volume m D = ----V m V = ------D m= DxV 2.2 – DENSITY - Sample Problem p 39 A piece of beeswax with a volume of 8.50 cm 3 is found to have a mass of 8.06 g. What is the density of the beeswax? m 8.06g D = --- = --------- = 0.948 g V 8.50cm3 cm3 (note: 3 sig.dig.) 2.2 – DENSITY - Sample Problem p 40 Cobalt is a hard magnetic metal that resembles iron in appearance. It has a density of 8.90 g/cm3. What volume would 17.8 g of cobalt have?
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