1 Physical Science Measurement Slides subject to change

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. m 2 ) Volume: cubic meters (abbr. m 3 )

3 Vitruvian Man (Leonardo da Vinci)

4 Metric System The international “decimalised” system of measurement was first adopted by France in Common system of measuring units used by most of the world. The international “decimalised” system of measurement was first adopted by France in 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. 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 Length Historically, in 1790, French must make a decision: Historically, in 1790, French must make a decision: 1 meter = length of a pendulum with a “half-period” of one second. 1 meter = length of a pendulum with a “half-period” of one second. OR OR 1 meter = one ten-millionth of the distance from the equator to the north pole. 1 meter = one ten-millionth of the distance from the equator to the north pole.

Dunkirk Barcelona

Meter So... distance was chosen. 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. 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 Became official in 1795, lasted to Today one meter equals the distance travelled by light in vacuum during a time interval of 1/299,792,458 of a second. 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 Lengths in Metric System Common multiples, submultiples: Common multiples, submultiples: kilometer (10 3 meter) kilometer (10 3 meter) centimeter (0.01 or meter) centimeter (0.01 or meter) millimeter (0.001 or 10 −3 meter) millimeter (0.001 or 10 −3 meter) micrometer (10 −6 meter) micrometer (10 −6 meter) nanometer (10 −9 meter) nanometer (10 −9 meter) larger >

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 International 1-kg Standard 1 gram (mass of 1.0 cm 3 H 2 O). 1 gram (mass of 1.0 cm 3 H 2 O). 1,000 grams is a kilogram. 1,000 grams is a kilogram. Exact mass kept in France. Exact mass kept in France. Accurate copy sent to U.S. in Accurate copy sent to U.S. in Platinum-iridium cylinder. Platinum-iridium cylinder. 1 kg = 2.2 lbs. 1 kg = 2.2 lbs.

More About Grams 1 gram = tiny cube of water. 1.0 cm X 1.0 cm X 1.0 cm. = 1.0 cm 3 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 kg.

12 Time Egyptians subdivided daytime into twelve hours since at least 2000 BC. Egyptians subdivided daytime into twelve hours since at least 2000 BC. Greeks divided a full day into 24 equal hours around 150 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 pars secunda minuta, second small part.

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

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

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

16 Major Submultiples, Multiples SubmultiplesMultiples centi kilo milli mega micro giga nano tera

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

18 Convert Units Convert 5 inches to centimeters Convert 5 inches to centimeters 5 in. = 5 in. x 1 5 in. = 5 in. x 1 = 5 in. x = 12.7 cm = 5 in. x = 12.7 cm 2.54 cm 1 in Use dimensional analysis to get the units straight. “Inches” cancel, leaving centimeters (cm). Use dimensional analysis to get the units straight. “Inches” cancel, leaving centimeters (cm).

19 Convert Speed Conversion factors: Conversion factors: 1 m = 3.28 ft 1 m = 3.28 ft 1 mile = 5280 ft 1 mile = 5280 ft What is 60 mi/hr in km/hr? What is 60 mi/hr in km/hr? x x x x x x = 97 km/hr = 97 km/hr 5280 ft 1 mi 1 m 3.28 ft 1 km 10 3 m 60 mi hr

20 Another Example Given 1 mile = 5,280 feet Given 1 mile = 5,280 feet What is 60 mi/hr in ft/s ? What is 60 mi/hr in ft/s ? x x x x x x = 88 ft/s = 88 ft/s 5280 ft 1 mi 1 hr 60 min 1 min 60 s 60 mi hr

21 Rounding Round 387 to “two places” Round 387 to “two places” Locate the digit in that place (the “8”). Locate the digit in that place (the “8”). Consider the digit to its right (the “7”). 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. 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. Answer is 390.

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

23 More about Sig Figs has two sig figs, has six, has four has two sig figs, has six, 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. 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.) 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: 5.66x10 8 has 3 sig figs. Scientific notation is relatively easy for significant figures: 5.66x10 8 has 3 sig figs.

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

25 An Equation: Density Density is the mass per unit volume of an object. Density is the mass per unit volume of an object. In Words: Density = Mass / Volume In Words: Density = Mass / Volume Symbols Symbols mass = m mass = m density = ρ density = ρ volume = V volume = V Equation ρ = m/V Equation ρ = m/V Example: Water density is 1.00 gram/cm 3. Example: Water density is 1.00 gram/cm 3. Greek letter “rho”

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