1. Chapter 1 Measurement, Models and Analysis

2. Definition of Physics: –Physics is the study of matter and energy and their relationships. What is the difference between pure science and applied science? –Pure science is: Studying a topic to gain knowledge or understand how something works. Examples: Electron flow, sun’s composition, structure of chromosomes

3. –Applied science is: The practical use of scientific information. Applied science can also be called technology. Examples: Electricity, Solar Power, Genetic Engineering

4. Pure ScienceApplied Science Question –What do we want to learn or understand? Hypothesis –An educated guess to answer the question. Experiment –Testing the hypothesis Analysis –Studying results to find patterns Conclusion –Do our results support our hypothesis? Problem –What do we want to change or improve?Design –A solution that we think will workTest –Build the design and see if it worksAnalysis –Evaluate the results of the testConclusion –Did the design work, or do we need changes? (the scientific method)(the engineering process)

5. Metric System (def): –A set of standards of measurement where units of different sizes are related by powers of 10. SI (def): –(Système Internationale d’Unités) International standards of measurement adapted from the metric system. Base Units (def): –The seven fundamental units of measure.

6. SI Base Units  Length  Mass  Time  Temperature  Amount of a Substance  Electric Current  Luminous Intensity  meter  kilogram  second  kelvin  mole  ampere  candela Base Quantity Base Unit Symbol mmmm  kg ssss KKKK  mol AAAA  cd

7. These units are the most commonly used units in Physics. They are in the MKS (meter-kilogram-second) system. –Two other systems are the CGS (centimeter- gram-second) system and the FPI (foot- pound-inch) system. We will be working mostly with the MKS system. Always remember to stick with the same measurement system through the whole problem.

8. Derived Units (def): –Unit of a quantity that is a combination of base units Examples: m/sec (unit of speed), kg·m 2 /sec 2 (joule, a unit of energy) Note that all base units are in the MKS system.

9. Review of Scientific Notation Format: M x 10 n where 1  M  10 and n is an integer. 1.Move the decimal point until one digit remains on the left. 2.The number of places you moved the decimal is |n|. 3.The direction that you moved the decimal determines the sign of the exponent n. a. If you moved the decimal to the right (the number is small), n is negative. 0.000000123 = 1.23 x 10 -7 b. If you moved the decimal to the left (the number is large), n is positive. 300,000,000 = 3.0 x 10 8

10. Adding/Subtracting Scientific Notation Adding/Subtracting numbers in scientific notation a.Make “n” the same between the numbers that you are adding or subtracting. b.Add or subtract “M”. c.Put your result in proper scientific notation and check significant figures.

11. Multiplying/Dividing Scientific Notation Multiplying or dividing numbers in scientific notation: a.Multiply or divide the “M” b.Add exponents if multiplying c.Subtract exponents if dividing d.Put your result in proper scientific notation and check significant figures.

12. Prefixes Used with SI Units teraT 1 000 000 000 00010 12 terameter (Tm) Multiplier Scientific PrefixSymbol(decimal)Notation Example gigaG 1 000 000 00010 9 gigameter (Gm) megaM 1 000 00010 6 megagram(Mg) kilok 100010 3 kilometer (km) centic 0.0110 -2 centimeter (cm) decid 0.110 -1 deciliter (dL) millim 0.00110 -3 milligram (mg) nanon 0.000 000 00110 -9 nanometer (nm) microμ 0.000 00110 -6 microgram (μg) picop 0.000 000 000 00110 -12 picometer (pm) femtof 0.000 000 000 000 00110 -15 femtosecond (fs)

13. Prefixes most commonly used in Physics are: –k, c, m Converting SI Units: move decimal right  → K H D base unit d c m  ← move decimal left

14. Factor Label Method Conversion Factor (def): –A multiplier equal to 1. Example:1 kg = 1000 g –Therefore: 1 kg 1000 g 1 kg = 1 The value of a quantity does not change when it is multiplied or divided by one. OR

15. Examples: a.1 Mg = ? g  “M” means mega Therefore, we can rewrite 1 Mg as 10 6 g Therefore, we can rewrite 1 Mg as 10 6 g b.13.76 μm = ? m  = 13.76 x 10 -6 m 1. Eliminating a Prefix

16. 2. Adding a Prefix : Use prefix table to create conversion factor. Example: a.13.7 m = ______ nm “n” = nano A conversion factor is a ratio that is equal to 1. For “nm”, we have two possibilities: Use the conversion factor that will cancel the units you need to eliminate: 1 nm 10 -9 m 1 nm = 1 OR 13.7 m x 1 nm 10 -9 m = 13.7 x 10 9 nm = 1.37 x 10 10 nm

17. 3. If you have more than one conversion in the problem, use multiple conversion factors. Example: a.Convert 1.1 cm to μm 1 cm = 10 -2 m 1 μm = 10 -6 m Conversion factors: = 1 1 cm 10 -2 m 1 cm = 1 OR = 1 μm 1 μm 10 -6 m μm 1 μm = 1 OR 1.1 cm x 10 -2 m 1 cm = 1.1 x 10 4 μm x μm 1 μm 10 -6 m

18. The equatorial rotation velocity of the earth is 465.11 m/s (meters per second). This is based on the sidereal rotation of earth, which is the reference rotation period used by scientists.

19. Trigonometry Review 1. The interior angles of a triangle total 180º. 2. Pythagorean theorem 3. Trig functions

20. The measuring tools that we will use most frequently are the meter stick, balance and stopwatch. The meter stick and balance should always be read with your eye directly in line with the device to avoid inaccuracy that results from parallax. Parallax (def): –The apparent shift in the position of an object when it is viewed from different angles. Measurement Uncertainties

21. In most cases, you read a device to the value of its finest division, then estimate one decimal beyond that. Device Finest division Measurement Meter stick1 mmx.x mm Balance0.1 g x.xx g Reading a stopwatch: For a stopwatch, you read what is given. No estimating is required.

22. Accuracy vs. Precision Accuracy –How well the results of an experiment agree with the measured and accepted value. Precision –The degree of exactness with which a quantity is measured using a given instrument. Sometimes indicated by the number of significant figures a measurement contains. Also has to do with the “repeatability” of the measurement data.

23. Accuracy vs. Precision For example, a 6-place table is more precise than a 4-place table. However, if there are errors in the 6-place table, it may be more or less accurate than the 4-place table. In many cases, when precision is high and accuracy is low, the fault can lie with the instrument.

24. Significant Digits (or Significant Figures) Significant Digits (def): –The valid digits in a measurement. Your answer can only be as exact as your least precise measurement. When taking the measurements, the estimated digit is significant.

25. Significant Digits (cont.) Zeroes – When are they significant? –Nonzero digits are always significant –All final zeros after the decimal point are significant, e.g. 354.0000 ( 7 sig figs) –Zeros between two other significant digits are always significant, e.g. 300004 (6 sig figs) –Zeros used solely as placeholders are not significant, e.g. 0.000009 (1 sig fig)

26. Significant Digits (cont.) How many significant figures are in each of the numbers below? 245 m → 3 sig figsRule 1 308 km → 3 sig figsRule 3 18.0 g → 3 sig figsRule 2 0.00623 m → 3 sig figsRule 4

27. Graphing Data Identify the independent and dependent variables in your data. The independent variable is plotted on the horizontal, or x-axis, the dependent variable is plotted on the vertical axis or y- axis. The title of your graph is written “y vs. x”. Determine the range of the independent variable to be plotted.

28. Decide whether the origin (0,0) is a valid data point. Spread the data out as much as possible. Let each division on the graph paper stand for a convenient unit. Number and label the horizontal axis. –The label should include the value name (e.g. time) and value units (e.g. seconds) Graphing Data

29. Repeat steps 2 – 5 for the dependent variable. Plot the data points on the graph. Draw the “best fit” straight line or smooth curve that passes through as many data points as possible. Do not use a series of straight line segments that “connect the dots.” Give the graph a title that clearly tells what the graph represents.