Fluent Essays

1. Compute, in centimeters and in meters, the height of a basketball player who is 6 ft 10 in. tall. ________________ cm  _________________m 2. Compute the density in g/cm3 of a piece of metal that has a mass of 0.490 kg and a volume of 78 cm3. ________________g/cm3 3.Round the following numbers to two significant figures. (a) 7.01 (b) 0.00100 (c) 9100. (d) 0.000321 4. Water is sold in one and a half liter bottles. What is the mass, in kilograms, of the water in such a full bottle? ___________________kg What is the mass, in grams, of the water in such a full bottle? ____________________g 5. A rectangular container measuring 23 cm ⨯ 38 cm ⨯ 57 cm is filled with water. What is the mass of this volume of water in kilograms and grams? ________________kg ________________g 6.Currently, the tallest building in the world is the Burj Khalifa (with 160 stories) in Dubai, United Arab Emirates, which is 828 m tall. Previously, the tallest was the Taipei 101 skyscraper (with 101 floors) in Taiwan, which is 508 m tall. Referring to the information above, how much shorter in feet is the Taipei 101 than the Burj Khalifa? ____________________ft 7.Compute the density in g/cm3 of a piece of metal that has a mass of 0.490 kg and a volume of 78 cm3. _________________g/cm3 8.In the figure below, is the conversion on the sign exact? Justify your answer. Maximum             was       Maximum 80                                             50 km/h                                      M.P.H THINKmetric Yes, the unit conversion for 80 km/h is exactly 50 mph. No, the unit conversion for 80 km/h is close to 50 mph but not exact. James T. Shipman Jerry D. Wilson Charles A. Higgins, Jr. Omar Torres © 2016 Cengage Learning Measurement Chapter 1 * © 2016 Cengage Learning Description leading to understanding of our environment Description involves the measurement of the physical world Understanding our environment demands the interpretation of accurate measurements (i.e., data) Therefore, understanding measurement is essential Intro Science * © 2016 Cengage Learning Sophisticated methods of measurement have been developed Measurements – movement, temperature, weather conditions, time, etc. The constant use of measurements are in this book, including many examples Can everything be measured with certainty? As smaller and smaller objects were measured it became apparent that the act of measuring actually distorted the object Intro Measurement * © 2016 Cengage Learning Subset of the Natural Sciences, together with Biological Sciences Physical Sciences: Physics, Chemistry, Geology, Meteorology, and Astronomy This book covers the fundamentals of each of the five Physical Sciences Section 1.1 What is Physical Science? * © 2016 Cengage Learning Section 1.1 The Major Physical Sciences * © 2016 Cengage Learning Measurements are the basis of scientific research/investigation Phenomena are observed, resulting in questions of how or why these phenomena occur Scientists assume that the universe is orderly and can be understood Section 1.2 Scientific Investigation * © 2016 Cengage Learning Scientific Method – general methods of observations, rules for reasoning, and making predictions Can be broken down into: Observations & Measurements Hypothesis Experiments Theory Law Section 1.2 Scientific Method * © 2016 Cengage Learning Quantitative data are gathered Section 1.2 Observations & Measurements * © 2016 Cengage Learning Hypothesis – a possible explanation for the observations Example: Matter consists of small particles (atoms) that simply rearrange themselves A tentative answer or educated guess New experiments are designed to test the validity of the hypothesis The Hypothesis is supported if it correctly predicts the experimental results Section 1.2 Hypothesis * © 2016 Cengage Learning The testing, under controlled conditions, to determine if the results support or confirm the hypothesis Experimental results can be duplicated by other researchers No concept or model of nature is valid unless the predictions are in agreement with experimental results. Section 1.2 Experiments * © 2016 Cengage Learning Theory – tested explanation for a broad segment of basic natural phenomena Example: Atomic Theory – This theory has withstood testing for 200+ years. Depending on continued experimentation, theories may be accepted, modified, or rejected Section 1.2 Theory * © 2016 Cengage Learning Scientific Law – after a series of experiments a concise statement (words/math) describes a fundamental relationship of nature Example – Law of Conservation of Mass (no gain or loss during chemical reaction) The law simply states the finding, but does not explain the behavior Section 1.2 Scientific Law * © 2016 Cengage Learning Section 1.2 The Scientific Method * © 2016 Cengage Learning Sight, hearing, smell, taste, touch Sight and hearing provide the most information to our brains about our environment Sensory limitations – can be reduced by using measuring devices Instruments extend our ability to measure and learn about our environment Our senses can also be deceived The Senses * © 2016 Cengage Learning Lines “a” and “b” are equal in length! Some Optical Illusions * © 2016 Cengage Learning Optical Illusions The lines are all horizontal! * © 2016 Cengage Learning Section 1.3 Some Optical Illusions * © 2016 Cengage Learning Section 1.3 Some Optical Illusions * © 2016 Cengage Learning Expressed in magnitude and units Fundamental quantities – length, mass, & time The study of Force and Motion requires only these three quantities Standard Unit – fixed and reproducible value to take accurate measurements Section 1.4 Standard Units and Systems of Units * © 2016 Cengage Learning Two major systems of units British (English) system – only used widely in the United States (miles, inches, pounds, seconds, etc.) Metric system – used throughout most of the world (kilometers, meters, grams, etc.) The U.S. “officially” adopted the metric system in 1893, but continues to use the British system Section 1.4 Standard Units and Systems of Units (cont.) * © 2016 Cengage Learning The measurement of space in any direction Space has three dimensions – length, width, and height Metric Standard Unit = Meter (m), originally defined as 1/10,000,000 of distance from equator to north pole British Standard Unit = Foot, originally referenced to the human foot Section 1.4 Length * © 2016 Cengage Learning Originally defined as a physical quantity of nature. 1/10,000,000 of the distance from the equator to the pole Section 1.4 The Meter * © 2016 Cengage Learning The meter is now defined by the distance light travels in a vacuum/time. The Meter * © 2016 Cengage Learning The amount of matter an object contains An object’s mass is always constant Mass is a fundamental unit that will remain constant throughout the universe Metric Standard Unit = Kilogram (kg) – originally defined as the amount of water in a 0.1-m cube. Now referenced to a cylinder in Paris Section 1.4 Mass (metric) * © 2016 Cengage Learning U.S. Prototype #20 Kilogram, at NIST in Washington, D.C. Actually – 0.999 999 961 kg Section 1.4 Kilogram Standard * © 2016 Cengage Learning British Standard Unit = Slug (rarely used) We use the Pound (lb) The pound is actually not a unit of mass, but rather of weight, related to gravitational attraction (depends on where the object is!) Object: Earth = 1 lb  Moon = 1/6 lb In fact, the weight of an object will vary slightly depending on where it is on Earth (higher altitude  less weight) Section 1.4 Mass (British) * © 2016 Cengage Learning Section 1.4 Mass is a Fundamental Quantity and Remains Constant – Weight Varies * © 2016 Cengage Learning Time – the continuous, forward flowing of events Time has only one direction  forward Second (s) – the standard unit in both the metric and British systems Originally 1/86,400 of a solar day Now based on the vibration of the Cs133 atom (Atomic Clock) Section 1.4 Time * © 2016 Cengage Learning Originally defined as a fraction of the average solar day. Section 1.4 A Second of Time * © 2016 Cengage Learning Defined by the radiation frequency of the Cs133 atom Section 1.4 A Second of Time * © 2016 Cengage Learning Uses acronym “mks system” from standard units of length, mass, and time – meter, kilogram, second It is a decimal (base-10) system – this is much better than the British system Administered by – Bureau International des Poids et Mesures (BIPM) in Paris International System of Units (SI) Contains seven base units Section 1.4 Metric System * © 2016 Cengage Learning The fundamental units are a choice of seven well-defined units which by convention are regarded as dimensionally independent: meter, m (length) kilogram, kg (mass) second, s (time) ampere, A (electrical current) kelvin, K (temperature) mole, mol (amount of a substance) candela, cd (luminous intensity) Section 1.5 Modern Metric System (SI) * © 2016 Cengage Learning Easy expression and conversion Metric examples vs. British examples 1 kilometer = 1000 meters 1 mile = 5280 feet 1 meter = 100 centimeters 1 yard = 3 feet or 36 inches 1 liter = 1000 milliliters 1 quart = 32 ounces or 2 pints 1 gallon = 128 ounces Section 1.5 Base-10  Convenient * © 2016 Cengage Learning Mega (M), 106  1,000,000 times the base Kilo (k), 103  1,000 times the base Centi (c), 10–2  1/100th of the base Milli (m), 10–3  1/1000th of the base See Appendix 1 for complete listing Section 1.5 Commonly Used Prefixes * © 2016 Cengage Learning Liter – volume of liquid in a 0.1-m (10 cm) cube (10 cm×10 cm×10 cm = 1000 cm3) A liter of pure water has a mass of 1 kg or 1000 grams Therefore, 1 cubic cm (cc) of water has a mass of 1 gram By definition 1 liter = 1000 milliliters (ml) So, 1 ml = 1 cc = 1 g of pure water 1 ml = 1 cc for all liquids, but other liquids do not have a mass of 1 g Section 1.5 Liter – Nonstandard Metric Unit * © 2016 Cengage Learning A liter is slightly more than a quart. 1 quart = 0.946 liter 1 liter = 1.06 quart Section 1.5 Liter & Quart * © 2016 Cengage Learning (1 kg = 2.2046 lb on Earth) The amount of water in a 0.10-m (10 cm) cube (0.10 m3) Section 1.5 The Kilogram * © 2016 Cengage Learning Metric ton – mass of 1 cubic meter (1 m3) of water 1 m = 100 cm (100 cm)3 = 1,000,000 cm3 Remember that 1000 cm3 = 1 liter Therefore, there are 1000 liters in 1 m3 of water Each liter has a mass of 1 kg 1 kg×1000 = 1 metric ton Section 1.5 Metric Ton * © 2016 Cengage Learning It is difficult to make all measurements with only the 7 fundamental units Derived units are therefore used, these are multiples/combinations of fundamental units We’ve already used derived units: Volume  length3, m3, cm3 Area  length2, m2, ft2, etc. Speed  length/time, m/s, miles/hour, etc. Section 1.6 Derived Units and Conversion Factors * © 2016 Cengage Learning Density () = mass per unit volume  = m/v [or mass/length3 (since v = length3)] Measures how “compact” a substance is Typical units used – g/cm3, kg/m3 Al = 2.7 g/cm3, Fe = 7.8 g/cm3, Au = 19.3 g/cm3 Average for the Earth = 5.5 g/cm3 Section 1.6 Density * © 2016 Cengage Learning Hydrometer – a weighted glass bulb The higher the hydrometer floats the greater the density of the liquid Pure water = 1 g/cm3 Seawater = 1.025 g/cm3 Urine = 1.015 to 1.030 g/cm3 Hydrometers are used to ’test’ antifreeze in car radiators – actually measuring the density of the liquid Section 1.6 Liquid Densities * © 2016 Cengage Learning The denser the liquid the higher the hydrometer floats. Section 1.5 Measuring Liquid Density * © 2016 Cengage Learning When a combination of units becomes complex and frequently used – It is given a name newton (N) = kg×m/s2 joule (J) = kg×m2/s2 watt (W) = kg×m2/s3 Section 1.6 Unit Combinations * © 2016 Cengage Learning Relates one unit to another unit Convert British to Metric (inches  cm) Convert units within system (kg  g) We use “conversion factors” 1 inch is equivalent to 2.54 centimeters Therefore “1 in. = 2.54 cm” is our conversion factor for inches & centimeters Section 1.6 Conversion Factors * © 2016 Cengage Learning Question: How many centimeters are there in 65 inches? Section 1.6 Since 1 in. = 2.54 cm  Or Easy Conversion – Example 65 in. × = 165 cm (the inches cancel out!!) * © 2016 Cengage Learning Step 1 – Choose/Use a Conversion Factor, generally can be looked up. Step 2 – Arrange the Conversion Factor into the appropriate form, so that unwanted units cancel out. Step 3 – Multiply or Divide to calculate answer. Use common sense – anticipate answer! Section 1.6 Steps to Convert or for example * © 2016 Cengage Learning How fast in mi/h is 50 km/h? Conversion Factor is 1 km/h = 0.621 mi/h Starting Value Conversion Factor Result Section 1.6 50 km/h  ?? mi/h * © 2016 Cengage Learning Section 1.6 50 km/h  ?? mi/h Starting Value Conversion Factor Result * © 2016 Cengage Learning Either conversion factor can be used: 1 km/h = 0.621 mi/h or 1 mi/h = 1.61 km/h How fast in km/h is 50 mi/h? Section 1.6 50 mi/h  ?? km/h Starting Value Conversion Factor Same Result * © 2016 Cengage Learning Section 1.6 50 mi/h  ?? km/h Starting Value Conversion Factor Same Result * © 2016 Cengage Learning 22 inches = ?? meters Inches  centimeters  meters Starting Value Conv. Factor #1 in  cm Conv. Factor #2 cm  m Result Section 1.6 Multi-Step Conversion – No Problem! * © 2016 Cengage Learning Section 1.6 Starting Value Conv. Factor #1 in.  cm Conv. Factor #2 cm  m Result Multi-Step Conversion – No Problem! * © 2016 Cengage Learning How would one express “First and 10” in meters? Conversion Factor is 1 yd = 0.914 m Section 1.6 Confidence Exercise 1.3 10 yd Starting Value × Conversion Factor yd m 1 914 . 0 = ?? Result * © 2016 Cengage Learning Section 1.6 = 9.14 m Result Confidence Exercise 1.3 (cont.) 10 yd Starting Value × Conversion Factor yd m 1 914 . 0 * © 2016 Cengage Learning 4843 m × = 15,885 feet above SL (1775 feet higher than the top of Pikes Peak!) Section 1.6 Peruvian Road Solution * © 2016 Cengage Learning Significant figures (“SF”) – a method of expressing measured numbers properly A mathematical operation, such as multiplication, division, addition, or subtraction cannot give you more significant figures than you start with For example, 6.8 has two SF and 1.67 has three SF Section 1.7 Significant Figures * © 2016 Cengage Learning When we use hand calculators we may end up with results like: 6.8 ÷ 1.67 = 4.0718563 Are all these numbers “significant?” Section 1.7 Significant Figures * © 2016 Cengage Learning General Rule: Report only as many significant figures in the result as there are in the quantity with the least significant figures. 6.8 cm ÷ 1.67 cm = 4.1 (round off 4.0718563) 6.8 is the limiting term with two SF 5.687 + 11.11 = 16.80 (round up 16.797) 11.11 is the limiting term with four SF Section 1.7 Significant Figures * © 2016 Cengage Learning All non-zero digits are significant Both 23.4 and 234 have 3 SF Zeros are significant if between two non-zero digits (’captive’) – 20.05 has 4 SF, 407 has 3 SF Zeros are not significant to the left of non-zero digits – used to locate a decimal point (leading zeros) – 0.0000035 has 2 SF To the right of all non-zero digits (trailing zeros), must be determined from context – 45.0 has 3 SF but 4500 probably only has 2 SF Section 1.7 Significant Figures – Rules * © 2016 Cengage Learning Exact Numbers – numbers of people, items, etc. are assumed to have an unlimited number of SF In the process of determining the allowed number of significant figures, we must generally also ’round off’ the numbers. Section 1.7 Significant Figures * © 2016 Cengage Learning If the first digit to be dropped is less than 5, leave the preceding digit unchanged. Round off to 3 SF: 26.142  26.1 If the first digit to be dropped is 5 or greater, increase the preceding digit by one. Round off to 3 SF: 10.063  10.1 Section 1.7 Rounding Off Numbers * © 2016 Cengage Learning Round off 0.0997 to two SF 0.0997  0.10 What about this? 5.0×356 = 1780 Round off 1780 to 2 SF 1780  1800 Section 1.7 Rounding off Numbers – Examples * © 2016 Cengage Learning Many numbers are very large or very small – it is more convenient to express them in ’powers-of-10’ notation See Appendix VI 1,000,000 = 10×10×10×10×10×10 = 106 Section 1.7 Powers-of-10 Notation (Scientific Notation) * © 2016 Cengage Learning Section 1.7 Examples of Numbers Expressed in Powers-of-10 Notation * © 2016 Cengage Learning The distance to the Sun can be expressed many ways: 93,000,000 miles 93×106 miles 9.3×107 miles 0.93×108 miles All four are correct, but 9.3×107 miles is the preferred format Section 1.7 Scientific Notation * © 2016 Cengage Learning The exponent, or power-of-10, is increased by one for every place the decimal point is shifted to the left. 360,000 = 3.6×105 The exponent, or power-of-10, is decreased by one for every place the decimal point is shifted to the right. 0.0694 = 6.94×10–2 Section 1.7 Rules for Scientific Notation * © 2016 Cengage Learning 5.6256×0.0012 = 0.0067507  round to 2 SF 0.0067507 rounds to 0.0068  change to scientific notation 0.0068 = 6.8×10–3 Section 1.7 Example – Rounding/Scientific Notation * © 2016 Cengage Learning 0.0024/8.05 = 0.0002981  round to 2 SF 0.0002981 rounds to 0.00030  change to scientific notation 0.00030 = 3.0×10–4 **Note that the “trailing zero” is significant** Section 1.7 Example – Rounding/Scientific Notation * © 2016 Cengage Learning Read the problem, and identify the chapter principle that applies to it. Write down the given quantities w/ units. Make a sketch. Determine what is wanted – write it down. Check the units, and make conversions if necessary. Survey equations – use appropriate one. Do the math, using appropriate units, round off, and adjust number of significant figures. Section 1.7 Problem Solving * © 2016 Cengage Learning The Earth goes around the Sun in a nearly circular orbit with a radius of 93 million miles. How many miles does Earth travel in making one revolution about the Sun? Section 1.7 Problem Solving * © 2016 Cengage Learning The Earth goes around the Sun in a nearly circular orbit with a radius of 93 million miles. How many miles does Earth travel in making one revolution about the Sun? Determine what parts of the question are important and how to attack the problem. Section 1.7 Problem – Example * © 2016 Cengage Learning The Earth goes around the Sun in a nearly circular orbit with a radius of 93 million miles. How many miles does Earth travel in making one revolution about the Sun? In order to solve this problem notice that you need an equation for a circular orbit (circumference, c) The radius, r, of 93,000,000 miles is given Our answer also needs to be in miles (convenient!) Equation: ( = 3.14159…) Section 1.7 Problem – Example * © 2016 Cengage Learning Circumference = ( = 3.14159…) c = 2×3.14159×93,000,000 miles or c = 2×3.14159×9.3×107 miles c = 58.433574×107 miles round off and adjust to two SF c = 5.8×108 miles 5.8×108 miles = distance that the Earth travels in one revolution around the Sun Section 1.7 Problem Solving * © 2016 Cengage Learning Important Equation Density:  = m/V Section 1.7 * 2.54 cm 1 in. 1 inch 1 2.54 cm = 2.54 cm 1 1 inch = 2.54 cm 1 inch 1 inch 2.54 cm 0.621 mi/h 50 km/h31.05 mi/h 1 km/h ´= 0.621 mi/h 50 km/h31.05 mi/h 1 km/h ´= 1.61 km/h 50 mi/h80.5 km/h 1 mi/h ´= 1 km/h 50 mi/h80.5 km/h 0.621 mi/h ´= 1.61 km/h 50 mi/h80.5 km/h 1 mi/h ´= 1 km/h 50 mi/h80.5 km/h 0.621 mi/h ´= 2.54 cm1 m 22 in.0.56 m 1 in.100 cm ´´= 2.54 cm1 m 22 in.0.56 m 1 in.100 cm ´´= 3.28 ft 1 m 6 6 11 0.00000110 1,000,00010 - === 2 cr p = 2 cr p =