Chapter 1

1. Chapter 1 The Physics Tool Kit

2. Objectives: • Explain need for standardization of measurement • Use metric system • Convert measurements • Solve problems using length, area, and volume • Distinguish between mass and weight • Use significant digits to determine accuracy • Differentiate between accuracy and precision • Solve problems using correct significant digits • Use a systematic approach to solving physics problems • Analyze problems using the problem-solving method

3. Standards of Measure • Sets of units of measure for length, weight, and other quantities defined in a way that is useful to a large number of people • Many standards have been used throughout history

4. Introduction to the Metric System • SI (International System of Units of Measurement) ≈ metric system • Gabriel Mouton credited for originating metric system • Decimal or base 10 system (easy to use) • Add prefixes to basic units • Can convert between simply by moving decimal point

5. Length • Basic unit of length is meter (or metre as in book); Abbreviated as “m” • Defined as the length of path traveled by light in a vacuum during a time interval of 1/299,792,458 of a second • For long distances, use kilometer = 1000 meters (Similar to mile)

6. Short distances, use centimeter = 1/100 or a meter (Similar to inch) • Millimeter used to measure very small distances • Conversion factor used to change from one set of units to another. Can also use dimensional analysis.

7. Area and Volume • Equations for areas/volumes of different shapes are found in inside back cover of book. • Be sure units are the same before you plug into equation. • The units for area on the result will be squared, for example m², cm², or in². Area is the number of square units it contains.

8. The units for volume on the result will be cubed, i.e. m³, cm³, or in³. • Volume is the number of cubic units. • V= LWH, or can use water displacement to measure. • When converting between units, be sure to cube the conversion factor!

9. Mass and Weight • Mass is the quantity of material making up an object • Mass is constant! • Basic unit of mass in metric system is kilogram (1000 grams) • A gram is defined as the mass of 1 cm³ of water at its maximum density. • For very small quantities, use milligram (1/1000 of a gram).

10. For very large quantities, use metric ton (1000 kg). • Measure using a balance. • Weight is a measure of the gravitational force or pull acting on an object. • Metric unit of weight is the Newton. • Measure using a spring balance.

11. Time • Based on movement of the Earth and the moon. • Basic unit of time is the second.

12. BASIC UNITS

13. Metric Prefixes Kilo- hecto- deka- UNIT deci- centi- milli- k h dk d c m Move decimal point left Move decimal point right Power of 10 between each increment

14. 1. What is the prefix for .01? • Deci • Centi • Milli • micro

15. Figure 5.1: Comparison of English and metric units.

16. Figure 5.2: Cube representations.

17. Figure 5.3:A 100 mL graduated cylinder. 1 mL = 1 cm3 1 milliliter = 1 cubic centimeter 100 mL = 100 cm3

18. Significant Digits and Accuracy • Exact numbers – number determined by counting or definition • Approximate numbers – number determined by measurement or estimation • Accuracy – number of digits we are reasonably sure of having counted

19. Called significant digits • The greater the number of significant digits, the better the accuracy • See page 37 for determining the number of significant digits

20. Figure 5.5: Measuring a pin. Reading is between 2.8 cm & 2.9 cm These divisions were visualized 2.85 cm is measurement “5” is uncertain

21. Significant Figures • Includes all numbers recorded in a measurement • For pin, length = 2.85 cm: 3 significant figures • All certain numbers plus first uncertain • Assume to be accurate to ± 1 in last # • Pin length is 2.85 ± 0.01 cm • Pin is somewhere between 2.84 & 2.86 cm

22. Precision • Precision – smallest unit with which measurement is made, or the position of the last significant digit • Accuracy is the number of digits(significant). The greater the # of digits, the better the accuracy. • Try not to confuse accuracy and precision (often have similar meanings)

23. Calculations with Measurements • The sum or difference of measurements can be no more precise than the least precise measurement • See rules for adding and subtracting top of page 41 • The product or quotient of measurements can be no more accurate than the least accurate measurement • See rules for multiplying and dividing top of page 42

24. Units do not have to be the same to multiply and divide • Units have to be the same to add or subtract • See rules for combining operations on page 43 • Procedures in book based on methods followed by American Association for Testing and Materials • This book will generally use three significant digits

25. Problem-Solving Method • In technical fields, problem-solving is more than plugging numbers into equations • Understanding principle involved in solving a problem more important • Must be able to take data, analyze problem, and find solution in orderly manner

26. Summary of Problem-Solving Method • Read problem carefully (2 times) • Make a sketch • Write all given information – don’t forget units! • Determine unknown – what are you trying to find out • Write basic equation or formula that relates • Find working equation by solving basic equation for unknown • Substitute into equation – include units! • Work out equation • Check your answer – ask “Does this make sense?”

27. 2. A new born baby usually is about 45 ______ long • Km • m • cm • mm

28. 3. 1 km is how many m? • 1 • 10 • 100 • 1000

29. 4. 1 cm is how many mm? • 1 • 10 • 100 • 1000