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Physics

Physics. Topic #1 MEASUREMENT & MATHEMATICS. Scientific Method. Problem to Investigate Observations Hypothesis Test Hypothesis Theory Test Theory Scientific Law  Mathematical proof. Measurement & Uncertainty. Uncertainty: No measurement is absolutely precise Estimated Uncertainty:

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Physics

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  1. Physics Topic #1 MEASUREMENT & MATHEMATICS

  2. Scientific Method • Problem to Investigate • Observations • Hypothesis • Test Hypothesis • Theory • Test Theory • Scientific Law  Mathematical proof

  3. Measurement & Uncertainty • Uncertainty: • No measurement is absolutely precise • Estimated Uncertainty: • Width of a board is 8.8cm +/- 0.1cm • 0.1cm represents the estimated uncertainty in the measurement • Actual width  between 8.7-8.9cm

  4. Measurement & Uncertainty • Percent Uncertainty: • Ratio of the uncertainty to the measured value, x 100 • Example: • Measurement = 8.8 cm • Uncertainty = 0.1 cm • Percent Uncertainty =

  5. Is the diamond yours? A friend asks to borrow your precious diamond for a day to show her family. You are a bit worried, so you carefully have your diamond weighed on a scale which reads 8.17 grams. The scale’s accuracy is claimed to be +/- 0.05 grams. The next day you weigh the returned diamond again, getting 8.09 grams. Is this your diamond?

  6. Scale Readings - Measurements do not necessarily give the “true” value of the mass - Each measurement could have a high or low by up to 0.05g - Actual mass of your diamond  between 8.12g and 8.22g Reasoning: (8.17g – 0.05g = 8.12g) (8.17g + 0.05g= 8.22g)

  7. * Actual mass your diamond - Between 8.12g and 8.22g * Actual mass of the returned diamond - 8.09g +/- 0.05g  Between 8.04g and 8.14g ** These two ranges overlap  not a strong reason to doubt that the returned diamond is yours, at least based on the scale readings

  8. Accuracy, Precision, and Percent Error ACCURACY- How close a measurement comes to the TRUE value PRECISION- How close a SERIES of measurements are to ONE ANOTHER PERCENT (%) ERROR-Absolute value of the theoretical minus the experimental, divided by the theoretical, multiplied by 100 Theoretical - Experimental / Theoretical x 100

  9. Metric System • Expanded & updated version of the metric system: Systeme International d’Unites

  10. Fundamental SI Units Physical QuantityNameAbbreviation Length meter m Mass kilogram kg Time second s Temperature Kelvin K Electric current ampere A Amt of Substance mole mol Luminous Intensity candela cd

  11. Metric System

  12. SI Prefixes Little Guys Big Guys

  13. Reference Table

  14. Scientific Notation • Alternative way to express very large or very small numbers • Number is expressed as the product of a number between 1 and 10 and the appropriate power of 10. Large Number: 238,000. = 2.38 x 105 Decimal placed between 1st and 2nd digit Small Number : 0.00043 = 4.3 x 10-4

  15. Scientific Notation Express the following numbers in Scientific Notation 1. 3,570 2. 0.0055 3. 98,784 x 104 4. 45

  16. Scientific Notation • “Scientific Notation” or “Powers of Ten” • Allows the number of significant figures to be clearly expressed • Example: • 56, 800  5.68 x 104 • 0.0034  3.4 x 10-3 • 6.78 x 104  Number is known to an accuracy of 3 significant figures • 6.780 x 104  Number is known to an accuracy of 4 significant figures

  17. Scientific Notation • Multiplying Numbers in Scientific Notation • Multiply leading values • Add exponents • Adjust final answer, so leading value is between 1 and 10 • Dividing Numbers in Scientific Notation • Divide leading values • Subtract exponents • Adjust final answer, so leading value is between 1 and 10

  18. Scientific Notation • Adding & Subtracting Numbers in Scientific Notation • Adjust so exponents match • Then, add or subtract leading values only • Adjust final answer, so leading value is between 1 and 10

  19. Significant Figures • All of the important/necessary or reliably known numbers • GUIDELINES • Non-zero digits  always significant • Zeros at the beginning of a number  Not significant (Decimal point holders) • 0.0578 m 3 Significant Figures (5, 7, 8) • Zeros within the number  Significant • 108.7 m 4 Significant Figures (1, 0, 8, 7) • Zeros at the end of a number, after a decimal point  Significant • 8709.0 m 5 Significant Figures (8, 7, 0, 9, 0)

  20. Significant Figures • Non-zero integers • Always counted as significant figures **How many significant figures are there in 3,456? 4 Significant Figures

  21. Significant Figures ZEROS * Leading Zeros - Never significant 0.0486  3 Significant Figures 0.003  1 Significant Figure

  22. Significant Figures ZEROS * Captive zeros - Always significant 16.07  4 Significant Figures 10.98  4 Significant Figures 70.8  3 Significant Figures

  23. Significant Figures ZEROS * Trailing Zeros - Significant only if the number contains a decimal point 9.300  4 Significant Figures 1.5000  5 Significant Figures

  24. Converting Units • Physics problems require the use of the correct units • Conversion factors • Allow you to change from one unit of measurement to another • Ex: 1 foot = 12 inches • Converting units • Choose the appropriate conversion factor • Multiply by the conversion factor as a fraction • Make sure units cancel!

  25. Derived Units Units for length, mass, and time (as well as a few others), are regarded as base SI units These units are used in combination to define additional units for other important physical quantities, such as force and energy  Derived Units

  26. Derived Unitswebsite • Units that are created based on formulas and equations • Volume • V= length·width·height = m·m·m = m3 • Area • A = length·width = m·m = m2 • Force • F = mass·acceleration = kg·m·s-2 = Newton, N • Work • W = Force·distance = N·m = Joule, J • Pressure • P = Force/Area = N·m-2 = Pascal, Pa

  27. Dimensional Analysis • Useful tool utilized to check the dimensional consistency of any equation to check whether calculations make sense • Length is represented by L • Mass is represented by M • Time is represented by T • For an equation to be valid, the left dimension must equal the right dimension

  28. Trigonometry • Pythagorean Theorem • Used to find the length of any side of a right triangle when you know the lengths of the other two sides • Right triangle  Triangle with a 90° angle • c2 = a2 + b2 • c = Length of the hypotenuse • a, b, = Lengths of the legs

  29. Trigonometric Functions • sin θ = opposite/hypotenuse • cos θ = adjacent/hypotenuse • tan θ = opposite/adjacent

  30. Trigonometric Functions • If you know the ratio of lengths of 2 sides of a right triangle, you can use inverse functions to determine the angles of that triangle • θ = arcsin (opposite/hypotenuse) • θ = arccos (adjacent/hypotenuse) • θ = arctan (opposite/adjacent) • Often written: sin−1, cos−1, tan−1

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