Introduction. The Scientific Method and Measurement

Transcription

1 Introduction The Scientific Method and Measurement

2 Defining How We Look At The Universe Observation: seeing an event or process in nature we wish to explain Hypothesis: a tentative explanation based on previous knowledge (experience) Theory: allows prediction of the outcome of future tests of the hypothesis

3 Developing a Theory Test the Hypothesis: set up experiments designed to tell you if the hypothesis is correct Repeating tests: after many different tests, assume the hypothesis is correct Try to Predict: See if the hypothesis allows prediction for new circumstances

4 Measurement Precision is indicated by significant figures Arithmetic rules for precision differ for addition/subtraction and multiplication/division

5 Addition and Subtraction When combining numbers, round or truncate the answer based on the data with the fewest decimal places cm cm = cm

6 Multiplying and Dividing When multiplying or dividing, the answer is expressed with the same number of significant figures as the data with the least number of significant figures units X units = units 4 significant figures units

7 Significant Figures Trapped Zeros are significant: Zeros to the right of digits and decimals are significant Zeros to the left are not significant

8 Determining the Number of Significant Figures PROBLEM: For each of the following quantities, underline the zeros that are significant figures(sf), and determine the number of significant figures in each quantity. For (d) to (f) express each in exponential notation first. (a) L (b) g (c) ml (d) m (e) 57,600. s (f) cm 3 PLAN: Determine the number of sf by counting digits and paying attention to the placement of zeros. SOLUTION: (a) L 2sf (b) g 4sf (c) ml 5sf (d) m (e) 57,600. s (f) cm 3 (d) 4.715x10-5 m 4sf (e) x10 4 s 5sf (f) 7.160x10-7 cm 3 4sf

9 Rules for Significant Figures in Answers 1. For addition and subtraction. The answer has the same number of decimal places as there are in the measurement with the fewest decimal places. Example: adding two volumes 83.5 ml ml ml = ml Example: subtracting two volumes ml ml ml = ml

10 Rules for Rounding Off Numbers 1. If the digit removed is more than 5, the preceding number increases by rounds to 5.38 if three significant figures are retained and to 5.4 if two significant figures are retained. 2. If the digit removed is less than 5, the preceding number is unchanged rounds to if three significant figures are retained and to 0.24 if two significant figures are retained. 3.If the digit removed is 5, the preceding number increases by 1 if it is odd and remains unchanged if it is even rounds to 17.8, but rounds to If the 5 is followed only by zeros, rule 3 is followed; if the 5 is followed by nonzeros, rule 1 is followed: rounds to 17.6, but rounds to Be sure to carry two or more additional significant figures through a multistep calculation and round off only the final answer.

11 Significant Figures and Rounding PROBLEM: Perform the following calculations and round the answer to the correct number of significant figures. (a) cm cm cm (b) 1 g 4.80x10 4 mg 1000 mg cm 3 PLAN: In (a) we subtract before we divide; for (b) we are using an exact number. SOLUTION: cm cm (a) 2 = cm cm 2 = cm cm (b) 4.80x10 4 mg cm 3 1 g 1000 mg = 48.0 g cm 3 = 4.16 g/ cm 3

12 Rules for Significant Figures in Answers 2. For multiplication and division. The number with the least certainty limits the certainty of the result. Therefore, the answer contains the same number of significant figures as there are in the measurement with the fewest significant figures. Multiply the following numbers: 9.2 cm x 6.8 cm x cm = cm 3 = 23 cm 3

13 Scientific Notation Standard notation : N X 10 x where N is 1 to 9 and x =+/- integers 1.0 x x 10 3 is NOT standard (2.5 x 10 4 is ).025 x 10 1 is NOT standard ( 2.5 x 10-1 is )

14 Shorthand Number Notation x 10 0 = x 10 3 = The exponent (x) is the number of decimal places moved to get standard notation from data

15 Counting places Move decimal place until it fits standard notation: x 10-4 moved decimal four places to the right x 10 3 moved decimal three places to the left

16 Rules for Scientific Notation Moving the decimal to the right produces a negative exponent, equal to the number of places moved Moving the decimal to the left produces a positive exponent equal to the number of places moved

17 Unit Dimensional Analysis Mathematical origin of units and conversion between units Factor-Label (dimensional analysis) method Consistency in measures

18 Converting to New Units 36 hrs x 60 min. x 60 sec. = sec. 1 hour 1 minute Conversion factors are unit definitions

19 Converting Distance Units 55 miles per hour to Kilometers per second 55 mi x 5,280 ft x 12 in x 2.54 cm x 1 m x hr mi ft in 100cm 1 Km x 1 hr x 1 min = Km/s 1000 m 60 min 60 sec = 2.5 x 10-2 Km /s

20 Unit Conversion S 5x10 What is the value of S in cm per second? 3 furlongs fortnight Conversion Factor: number with 2 different units of measure Solution requires convenient placement of conversion factors: S 5x10 3 furlongs fortnight x 1 mile 8 furlong 5280 feet x mile 12inches x foot x 2.54cm inch 1fortnight x 14days x 1day 24hours 1hour x 3600sec 83.15cm sec

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22 Standard Units of Measure

23 Common SI-English conversion factors Quantity SI Unit SI Equivalent English Equivalent English to SI Equivalent Length 1 kilometer(km) 1000(10 3 )m 0.62miles(mi) 1 mi = 1.61km Volume 1 meter(m) 100(10 2 )m 1.094yards(yd) 1000(10 3 )mm 39.37inches(in) 1 centimeter(cm) 0.01(10-2 )m in 1 kilometer(km) 1000(10 3 )m 0.62mi 1 cubic meter(m 3 ) 1,000,000(10 6 ) cubic centimeters 1 cubic decimeter (dm 3 ) 1 cubic centimeter (cm 3 ) 1000cm cubic feet (ft 3 ) gallon (gal) quarts (qt) 1 yd = m 1 foot (ft) = m 1 in = 2.54cm (exactly!) 1 mi. = 5,280 ft. 1 ft 3 = m 3 1 gal = dm 3 1 qt = dm dm fluid ounce 1 qt = cm 3 1 fluid ounce = 29.6 cm 3 Mass 1 kilogram (kg) 1000 grams 2,205 pounds (lb) 1 gram (g) 1000 milligrams ounce(oz) 1 (lb) = kg 1 lb = g 1 ounce = g

24 The Freezing and Boiling Points of Water

25 Conversion Factors o C = 5/9 ( o F-32) o F= 9/5 o C+32 Kelvin Temperature units: K= o C

26 At Boiling: o C = 5/9 (212 o 32) = 100 o C o F=9/5 * 100 o C + 32 = 212 O F

27 Common Decimal Prefixes Used with SI Units Prefix Prefix Symbol Number Word Exponential Notation tera T 1,000,000,000,000 trillion giga G 1,000,000,000 billion 10 9 mega M 1,000,000 million 10 6 kilo k 1,000 thousand 10 3 hecto h 100 hundred 10 2 deka da 10 ten one 10 0 deci d 0.1 tenth 10-1 centi c 0.01 hundredth 10-2 milli m thousandth 10-3 micro millionth 10-6 nano n billionth 10-9 pico p trillionth femto f quadrillionth 10-15

28 Densities of Some Common Substances Density = mass/volume Substance Physical State Density (g/cm 3 ) Hydrogen Gas Oxygen Gas Grain alcohol Liquid Water Liquid Table salt Solid 2.16 Aluminum Solid 2.70 Lead Solid 11.3 Gold Solid 19.3

29 Specific Gravity When the density of a substance is compared to the density of water(1.00g/ml), the units divide out. The resulting unit less number allows simple evaluation. The value of the specific gravity for any substance is equal to it s density (g/ml).

30 Energy Kinetic Energy- matter that is in motion has an energy associated with it that is related to the mass and the speed: K.E.= ½ mv 2

31 Potential Energy Stored energy Position provides potential for motion Energy stored in molecular substances such as fuel Nuclear emission used to heat steam that move turbines Results in kinetic energy if released!

32 Conservation of Matter and Energy Energy can neither be created nor destroyed Matter can be converted to energy The total energy of the universe is constant

33 Heat Energy Particles that make up matter can absorb energy and transfer energy in the form of heat. Associated with the absorption of heat energy is an increase in temperature. Heat energy causes the particles that make up matter to jiggle around more. (have more kinetic energy).

34 Measuring Heat The amount of heat energy required to raise the temperature of 1 gram of a substance by 1 degree Celsius is the SPECIFIC HEAT: We usually measure the temperature increase of water 1 Calorie = Joules Cal/g. o C

35 Thermochemistry The specific heat can be used to measure the amount of heat in a substance Temperature changes often occur with chemical reactions Amount of heat energy=sh x mass x (T 2 -T 1 ) where T 2 is the final temp and T 1 is the starting temp of the material.