Physical Science

1. 1 Measurement Slides subject to change Physical Science

2. 2 What to Measure? Fundamental Units such as Length (meter, abbr. m) Mass (kilogram, abbr. kg) Time (second, abbr. s) Derived Units such as Velocity: kilometers/hour, miles/hour Area: square meters (abbr. m2 ) Volume: cubic meters (abbr. m3)

3. 3 Vitruvian Man (Leonardo da Vinci)

4. 4 Metric System • The international “decimalised” system of measurement was first adopted by France in 1791. Common system of measuring units used by most of the world. • In the United States, metric units are widely used in science, military, and industry. Some names for metric system “mks” = m − kg − s or SI (“Le Système international d'unités”) or simply, the “metric system”

5. 5 Length • Historically, in 1790, French must make a decision: • 1 meter = length of a pendulum with a “half-period” of one second. • OR • 1 meter = one ten-millionth of the distance from the equator to the north pole.

6. Dunkirk Barcelona

7. Meter • So ... distance was chosen. • One meter defined in 1793 as the distance between two scratches on a metal bar in Paris, pending completion of the survey. • Became official in 1795, lasted to 1960. • Today one meter equals the distance travelled by light in vacuum during a time interval of 1/299,792,458 of a second. 7

8. 8 Lengths in Metric System • Common multiples, submultiples: • kilometer (103 meter) • centimeter (0.01 or 10-2 meter) • millimeter (0.001 or 10−3 meter) • micrometer (10−6 meter) • nanometer (10−9 meter) larger >

9. Compare to English • 1 inch = 2.54 cm (approx. width of your thumb) • 1 meter = 1.09 yard • Slightly more than three feet. • 100 meter race is longer or shorter than 100 yard race? • 1 kilometer = 0.6 mile • 10 km (10K) race is what distance in miles?

10. 10 International 1-kg Standard • 1 gram (mass of 1.0 cm3 H2O). • 1,000 grams is a kilogram. • Exact mass kept in France. • Accurate copy sent to U.S. in 1899. • Platinum-iridium cylinder. • 1 kg = 2.2 lbs.

11. More About Grams • 1 gram = tiny cube of water. • 1.0 cm X 1.0 cm X 1.0 cm. = 1.0 cm3 • In medicine this volume is called a “cc”–— “cubic centimeter.” • In drinking water, it is called a milliliter (ml). • Common bottle of water is 500 ml or 500 cc. Mass is 500 g or 0.500 kg.

12. 12 Time Egyptians subdivided daytime into twelve hours since at least 2000 BC. Greeks divided a full day into 24 equal hours around 150 BC. Hour subdivided into 60 units to what we call “minutes,” to 60ths of that − to what we call “seconds” − by the Babylonians after 300 BC. hour: Latin hora, hour, time, season.. minute: Latin pars minuta prima, first small part. second: Latin parssecunda minuta, second small part.

13. One Second • Today ... • Officially one second is related to the frequency of the radiation from cesium-133–the time to perform 9,192,631,770 oscillations. 

14. 14 Time in Metric • Common multiples, submultiples: • millisecond or “ms” (10-3 s) • microsecond or “μs” (10-6 s) • Minute (60 s) ... hmmm, this isn’t metric. • Hour (60 minutes) ... hmmm, this isn’t metric either.

15. 15 Metric 10-Hour Watch • What time is it? • Decimal time introduced during the French Revolution in the decree of October 5, 1793. • Midnight is 10 o’clock. • Noon is 5 o’clock. • 7:45:07 pm

16. 16 Major Submultiples, Multiples

17. 17 Convert Units • The power of “One” • Conversion factor: 2.54 cm = 1 inch • And so does ...

18. 18 Convert Units • Convert 5 inches to centimeters • 5 in. = 5 in. x 1 = 5 in. x = 12.7 cm • Use dimensional analysis to get the units straight. “Inches” cancel, leaving centimeters (cm).

19. 19 Convert Speed • Conversion factors: • 1 m = 3.28 ft • 1 mile = 5280 ft • What is 60 mi/hr in km/hr? • x x x • = 97 km/hr

20. 20 Another Example • Given 1 mile = 5,280 feet • What is 60 mi/hr in ft/s ? • x x x • = 88 ft/s

21. 21 Rounding • Round 387 to “two places” • Locate the digit in that place (the “8”). • Consider the digit to its right (the “7”). • If the digit to the right (the “7”) is 5 or higher, round up; if the digit to the right is less than 5 round down. • Answer is 390.

22. 22 Rounding Exercise • Round 3872.2459 to the nearest: • a. thousandth • b. hundredth • c. tenth • d. one • e. ten • f. hundred • g. thousand • View π(pi) on your calculator. Round to four significant figures.

23. 23 More about Sig Figs • 0.00052 has two sig figs, 1.00052 has six, 1.230 has four. • When we say one foot has 12 inches, the 12 is exact, don’t consider it when figuring the number of significant figures. • Assume values in text problems are exact, thus the text’s “100 miles” has three sig figs.) • Scientific notation is relatively easy for significant figures: 5.66x108 has 3 sig figs.

24. 24 Even More on Sig Figs • In multiplication or division, your answer will have lowest sig. figs. of the terms you are calculating. • 4.2 x 3.4159 - least significant figure term has 2 sig figs (14). • Answer is 14. (not 14.34678). • If you do the entire problem on your calculator, adjust the answer for significant figures at the end.

25. 25 An Equation: Density • Density is the mass per unit volume of an object. • In Words: Density = Mass / Volume • Symbols • mass = m • density = ρ • volume = V • Equation ρ = m/V • Example: Water density is 1.00 gram/cm3. Greek letter “rho”

26. 26 Density • A certain bar of gold has a mass of 9,650 g and volume of 500 cm3. What is its density (in g/cm3)? 1. Understand the problem. 2. Givens m = 9,650 g (√ right units) V = 500 cm3 (√ right units) 3. Potential Formula ρ = m/V 4. Solve ρ = 9,650 g / 500 cm3 = 19.3 g/cm3