Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Phys 250 Ch1 p1Measurement, Models and AnalysisPhysics: knowledge of natureModel: an idealized description of a physical system or natural phenomenaidealized how?simplifications?Measurements and Modelsqualitative vs. quantitative descriptionsinterplay between observation (measurements) and the development/refinement of model:the “scientific method”Phys 250 Ch1 p2Units and Standards of MeasurementHow big is ...A quantity has dimensions if the answer depends upon the units (inches, feet, cm, etc.)Basic Units or Fundamental Units are the standards by which measurement results are describedSymbols for units can be used to help with dimensional analysis by treating unit symbols algebraically:mssmssmssm505050510 Phys 250 Ch1 p3Prefixes for units are convenient shorthand for scientific notationcheck out http://www.wordwizz.com/pwrsof10.htmhttp://microcosm.web.cern.ch/Microcosm/P10/english/P0.htmlPhys 250 Ch1 p4Examples:A soccer field is supposed to be at least 100m x 64 m. What is the area (in kilometers squared) of the smallest legal field?What is the volume of a sheet of paper that is 21.6 cm by 27.9 cm and 8.6E-3 cm?Phys 250 Ch1 p5Consistency of unitsAlgebraic equations must always be dimensionally consistent.You can’t add apples and oranges!cminchcmftinchesftftinchcmcminch48.30540.212111540.2540.21converting unitstreat units as algebraic quantitiesmultiplying or dividing a quantity by 1 does not affect its value s5sm2m10 time speed distancevtdPhys 250 Ch1 p6Some Useful Conversion factors:1 inch = 2.54 cm1 m = 3.28 ft1 mile = 5280 ftExamples:How many kilometers are in one mile?If an automobile has a speed of 25 mi/h, what is its speed in km/s?Phys 250 Ch1 p7Significant Figures: common way of implicitly indicating uncertaintynumber is only expressed using meaningful digits (sig. figs.)last digit (the least significant digit = lsd) is uncertain3 one digit3.0 two digits (two significant figures = 2 sig. figs.)3.00 three digits,etc. (300 how many digits?)Combining numbers with significant digitsAddition and Subtraction: least significant digit determined by decimal places (result is rounded).57 + .3 = .87 =.9 11.2 - 17.63 = 6.43 = 6.4Multiplication and Division: number of significant figures is the number of sig. figs. of the factor with the fewest sig. figs.1.3x7.24 = 9.412 = 9.4 17.5/.3794 = 46.12546 = 46.1 Integer factors and geometric factors (such as ) have infinite precisionx 3.762 = 44.4145803 = 44.4Phys 250 Ch1 p8Examples:Calculate the volume of an cylindrical oatmeal box with a diameter of 10.2 cm and a height of 18.4 cmPhys 250 Ch1 p9Estimates and Order of magnitude calculationsan order of magnitude is a (rounded) 1 sig fig calculation, whose answer is expressed as the nearest power of 10.Estimates should be done “in your head”check against calculator mistakes!ExampleEstimate the volume of rubber worn from automobile tires each year in the United States. The average radial tire has a useful tread depth of 5/16 in and can be driven 35,000 mi before it is worn out.Phys 250 Ch1 p10Succeeding in Physics:Physics is about applying principles to solve problems! learn definitionsdo problemsProblem solving strategiesRead the entire problem carefullydraw a (simple) diagramidentify what is givenexplicit informationimplicit informationfind mathematical relation(s) between known and unknown quantitiessolve the equations (and watch units!)reality