![ Density (r) = mass per unit volume
r=m/v [or m/length3
(since v = length3
)]
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 solid earth = 5.5 g/cm3
Section 1.6](https://image.slidesharecdn.com/sci1010chapter1-130823111152-phpapp02/85/Sci-1010-chapter-1-41-320.jpg)
Sci 1010 chapter 1
- 1. Chapter 1
- 2. 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
- 3. 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 w/ certainty?? As smaller and smaller objects were measured it became apparent that the act of measuring actually distorted the object. Intro
- 4. 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
- 5. Section 1.1
- 6. 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
- 7. 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
- 8. Quantitative data are gathered Section 1.2
- 9. 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
- 10. 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
- 11. 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
- 12. 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
- 13. Section 1.2
- 14. 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 -> Section 1.3
- 15. Lines “a” and “b” are equal in length! Section 1.3
- 16. The lines are all horizontal! Section 1.3
- 17. Section 1.3
- 18. Section 1.3
- 19. 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
- 20. 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
- 21. Section 1.4
- 22. 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
- 23. Originally defined as a physical quantity of nature. 1/10,000,000 of the distance from the equator to the pole. Section 1.4
- 24. The meter is now defined by the distance light travels in a vacuum/time. Section 1.4
- 25. 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 0.1m cube. Now referenced to a cylinder in Paris Section 1.4
- 26. U.S. Prototype #20 Kilogram, at NIST in Washington, D.C. Actually – 0.999 999 961 kg of “the” standard in Paris Section 1.4
- 27. 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 = 1lb. Moon = 1/6lb. In fact, the weight of an object will vary slightly depending on where it is on earth (higher altitude less weight) Section 1.4
- 28. Section 1.4
- 29. 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
- 30. Originally defined as a fraction of the average solar day. Section 1.4
- 31. Defined by the radiation frequency of the Cs133 atom Section 1.4
- 32. 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
- 33. 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
- 34. 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
- 35. 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
- 36. Liter – volume of liquid in a 0.1m (10 cm) cube (10cm x 10cm x 10cm = 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
- 37. A Liter is slightly more than a quart. – 1 quart = .946 liter – 1 liter = 1.06 quart Section 1.5
- 38. (1 kg = 2.2046 lb on earth) The amount of water in a 0.10m (10 cm) cube (0.10m3 ) Section 1.5
- 39. Metric ton -- mass of 1 cubic meter (1 m3 ) of water 1 m = 100 cm (100cm)3 = 1,000,000 cm3 Remember that 1000 cm3 = liter Therefore, there are 1000 liters in 1 m3 of water. Each liter has a mass of 1 kg. 1 kg x 1000 = 1 metric ton Section 1.5
- 40. 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
- 41. Density (r) = mass per unit volume r=m/v [or m/length3 (since v = length3 )] 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 solid earth = 5.5 g/cm3 Section 1.6
- 42. Hydrometer – a weighted glass bulb The higher the hydrometer floats the greater the density of the liquid Pure water = 1g/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
- 43. The denser the liquid the higher the hydrometer floats. Section 1.5
- 44. When a combination of units becomes complex and frequently used – It is given a name ◦ newton (N) = kg x m/s2 ◦ joule (J) = kg x m2 /s2 ◦ watt (W) = kg x m2 /s3 Section 1.6
- 45. Relates one unit to another unit Convert British to Metric (1in cm) Convert units within system (1kg g) We use “conversion factors” – many are listed on inside back cover of book 1 inch is equivalent to 2.54 centimeters Therefore “1 in = 2.54 cm” is our conversion factor for inches & centimeters Section 1.6
- 46. Question: How many centimeters are there in 65 inches? Section 1.6 2.54 cm = 11 inch • Since 1 in = 2.54 cm 1 in 2.54 cm = 1• Or 2.54 cm 1 in • 65 in. x = 165 cm (the inches cancel out!!)
- 47. 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! cm inch 54.2 1 or inch cm 1 54.2 for example Section 1.6
- 48. How fast in mi/h is 50 km/h? Conversion Factor is 1km/h=0.621mi/h 50 km/h Starting Value hkm hmi /1 /621.0 x Conversion Factor = 31.05 mi/h Result Section 1.6
- 49. Section 1.6 50 km/h Starting Value hkm hmi /1 /621.0 x Conversion Factor = 31.05 mi/h Result
- 50. Either Conversion Factor can be used: 1km/h = 0.621mi/h or 1mi/h = 1.61km/h How fast in km/h is 50 mi/h? hmi hkm /621.0 /1 50 mi/h x = 80.5 km/h Starting Value Conversion Factor Same Result 50 mi/h x hmi hkm /1 /61.1 = 80.5 km/h Section 1.6
- 51. Section 1.6 hmi hkm /621.0 /1 50 mi/h x = 80.5 km/h Starting Value Conversion Factor Same Result 50 mi/h x hmi hkm /1 /61.1 = 80.5 km/h
- 52. 22 inches = ?? Meters Inches centimeters meters 22 in Starting Value in cm 1 54.2 x Conv. Factor #1 in cm cm m 100 1 x Conv. Factor #2 cm m = 0.56 m Result Section 1.6
- 53. Section 1.6 22 in Starting Value in cm 1 54.2 x Conv. Factor #1 in cm cm m 100 1 x Conv. Factor #2 cm m = 0.56 m Result
- 54. How would one express “First and 10” in meters? Conversion Factor is 1yd = 0.914 m 10 yd Starting Value Section 1.6 x Conversion Factor yd m 1 914.0 = ?? Result
- 55. 10 yd Starting Value Section 1.6 x Conversion Factor yd m 1 914.0 = 9.14 m Result
- 56. Photo Source: Copyright © Bobby H. Bammel. All rights reserved. Section 1.6
- 57. 4843 m x m ft 1 28.3 = 15,885 feet above SL (1775 feet higher than the top of Pikes Peak!) Section 1.6
- 58. 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
- 59. 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
- 60. General Rule: Report only as many significant figures in the result as there are in the quantity with the least. 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
- 61. 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
- 62. 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
- 63. 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
- 64. Round off 0.0997 to two SF 0.0997 0.10 What about this? 5.0 x 356 = 1780 Round off 1780 to 2 SF 1780 1800 Section 1.7
- 65. Many numbers are very large or very small – it is more convenient to express them in ‘powers-of-10’ notation 1,000,000 = 10x10x10x10x10x10 = 106 Section 1.7 000,000,1 1 6 10 1 = = 0.000001 = 10-6
- 66. Section 1.7 Standard HMCO copyright line
- 67. The distance to the sun can be expressed many ways: ◦ 93,000,000 miles ◦ 93 x 106 miles ◦ 9.3 x 107 miles ◦ 0.93 x 108 miles All four are correct, but 9.3 x 107 miles is the preferred format. Section 1.7
- 68. 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 x 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 x 10-2 Section 1.7 Rules for Scientific Notation
- 69. 5.6256 x 0.0012 = 0.0067507 round to 2 SF 0.0067507 rounds to 0.0068 change to scientific notation 0.0068 = 6.8 x 10-3 Section 1.7 Example Rounding/Scientific Notation
- 70. 0.0024/8.05 = 0.0002981 round to 2 SF 0.0002981 rounds to 0.00030 change to scientific notation 0.00030 = 3.0 x 10-4 **Note that the “trailing zero” is significant** Section 1.7 Example Rounding/Scientific Notation
- 71. 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
- 72. 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
- 73. 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
- 74. 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) The radius of 93,000,000 miles is given Our answer also needs to be in miles (convenient!) Equation: c = 2pr (p = 3.14159…) Section 1.7 Problem Example
- 75. Circumference = c = 2pr (p = 3.14159…) c = 2 x 3.14159 x 93,000,000 miles or c = 2 x 3.14159 x 9.3 x 107 miles c = 58.433574 x 107 miles round off and adjust to two SF c = 5.8 x 108 miles 5.8 x 108 miles = distance that the earth travels in one revolution around the sun Section 1.7 Problem Solving
- 76. Density: r = m/V Section 1.7