chapter 1 measurement - illinois state universitybkc/phy102/introandmeas.pdf · derived units and...
TRANSCRIPT
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James T. ShipmanJerry D. WilsonCharles A. Higgins, Jr.
Measurement
Chapter 1
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Small Scale
1 - 2 meters, the average human
2 centimeter, 10-2 m, a penny
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0.1 mm, 10-4 m, the thickness of 1or 2 pieces of paper
10-6 m, the wavelength of visible light
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10-8 m, virus or large molecule
10-10 m, small molecule
10-15 m, nucleus or black hole
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Large Scale
100 m,102 m, length of a football field
10 km, 104 m, length of Bloomington-Normal or diameter of a neutron star
106 m, length of Yugoslavia, distance from Normal to Baltimore, Raleigh, and Dallas
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108 m, 1/4 the way to the moon, radius of Saturn, distance light travels in 1/3 second
1010 m, 1/6 the distance from the sun to mercury, distance light travels in 33 seconds
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1012 m, distance from sun to halfway between Jupiter and Saturn, 1/6 the way to Pluto, 1 light hour
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1016 m, 1/4 the way to the nearest star, 1 light year
1020 m, 1/3 the way to the center of our galaxy, 10000 ly
1022 m, 10 times the diameter of the Milky Way, 1/2 the way to the Andromeda galaxy, 6 times the way to the Megallanic Clouds
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1024 m, roughly the distance to the next cluster of galaxies, 100 million ly
1026 m, 10 Bly, 10000 Mly, 1/3 to 1/2 the age of the Universe
Remember, light that we see coming from objects 10 Bly distant is from objects that no longer exist in the form that we see...
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Science
• 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
Audio Link
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Measurement
• 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
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What is Physical Science?
• 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
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What is Physical Science?
• 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
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The Major Physical Sciences
Section 1.1
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The Scientific Method(the short version)
Observation Develop a model that includes a mechanism Predict new phenomenon and explain diverse
observations with new model Modify model based on discrepancies Repeat ad infinitum
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Scientific Investigation
• 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
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Scientific Method
• 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
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Observations & Measurements
• Quantitative data are gathered
Section 1.2
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Hypothesis
• 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
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Experiments
• 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
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Theory
• 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
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Scientific Law
• 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
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The Scientific Method
Section 1.2
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The Senses
• 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 ->
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Some Optical Illusions
Lines “a” and “b” are equal in length!
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Optical Illusions
The lines are all horizontal!
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Some Optical Illusions
Section 1.3
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Some Optical Illusions
Section 1.3
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Standard Unitsand Systems of Units
• 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
Audio Link
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Standard Unitsand Systems of Units continued…
• 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
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Length
• 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
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The Meter
Originally defined asa physical quantity of nature.
1/10,000,000 of the distance from the equator to the pole.
Section 1.4
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The Meter
The meter is now defined by the distance light travels in a vacuum/time.
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Mass (metric)
• 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
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Kilogram Standard
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
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Mass (British)
• 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
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Mass is a Fundamental Quantity and Remains Constant - Weight
Varies
Section 1.4
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Time
• 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
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A Second of Time
Originally defined as a fraction of the average solar day.
Section 1.4
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A Second of Time
Defined by the radiation frequency of the Cs133 atom
Section 1.4
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Metric System
• 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
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Modern Metric System (SI)
• 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
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Base-10 Convenient
• 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
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Commonly Used Prefixes
• 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
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Liter – Nonstandard Metric Unit
• 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
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Liter & Quart
• A Liter is slightly more than a quart.– 1 quart = .946 liter– 1 liter = 1.06 quart
Section 1.5
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The Kilogram
• (1 kg = 2.2046 lb on earth)
• The amount of water in a 0.10m (10 cm) cube (0.10m3)
Section 1.5
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Metric Ton
• 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
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Derived Units and Conversion Factors
• 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
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Density
• Density (ρ) = mass per unit volume • ρ =m/v [or m/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 solid earth = 5.5 g/cm3
Section 1.6
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Liquid Densities
• 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
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Measuring Liquid Density
• The denser the liquid the higher the hydrometer floats.
Section 1.5
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Unit Combinations
• 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
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Conversion Factors
• 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
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Easy Conversion Example
• Question: How many centimeters are there in 65 inches?
Section 1.6
2.54 cm= 11 inch• Since 1 in = 2.54 cm
1 in2.54 cm
= 1• Or
2.54 cm1 in
• 65 in. x = 165 cm (the inches cancel out!!)
Audio Link
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Steps to Convert
• 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!
1 inch2 .54 cm or
2 .54 cm1 inch
for example
Section 1.6
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50 km/h ?? mi/h
• How fast in mi/h is 50 km/h? • Conversion Factor is 1km/h=0.621mi/h
50 km/h
Starting Value
0 .621mi /h1 km /h
x
ConversionFactor
= 31.05 mi/h
Result
Section 1.6
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50 km/h ?? mi/h
Section 1.6
50 km/h
Starting Value
0 .621mi /h1 km /h
x
ConversionFactor
= 31.05 mi/h
Result
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50 mi/h ?? km/h
• 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?
1 km /h0 .621mi /h
50 mi/h x = 80.5 km/h
Starting Value ConversionFactor
SameResult
50 mi/h x1 . 61km /h
1mi / h= 80.5 km/h
Section 1.6
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50 mi/h ?? km/h
Section 1.6
0 .621mi /h1 km /h
50 mi/h x = 80.5 km/h
Starting Value ConversionFactor
SameResult
50 mi/h x1 . 61km /h
1mi / h= 80.5 km/h
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Multi-Step ConversionNo Problem!
• 22 inches = ?? Meters• Inches centimeters meters
22 in
Starting Value
2 .54 cm1 in
x
Conv. Factor #1in cm
1m100cm
x
Conv. Factor #2cm m
= 0.56 m
Result
Section 1.6
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Multi-Step ConversionNo Problem!
Section 1.6
22 in
Starting Value
2 .54 cm1 in
x
Conv. Factor #1in cm
1m100cm
x
Conv. Factor #2cm m
= 0.56 m
Result
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Confidence Exercise 1.3
• How would one express “First and 10” in meters?
• Conversion Factor is 1yd = 0.914 m
10 yd
Starting Value
Section 1.6
x
ConversionFactor
yd
m
1
914.0= ??
Result
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Confidence Exercise 1.3 (cont)
10 yd
Starting Value
Section 1.6
x
ConversionFactor
yd
m
1
914.0= 9.14 m
Result
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Peruvian Road Solution
4843 m x3. 28 ft1m = 15,885 feet above SL
(1775 feet higher than the top of Pikes Peak!)
Section 1.6
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Significant Figures
• 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
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• 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
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• 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
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Significant Figures - Rules
• 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
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Significant Figures
• 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
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Rounding Off Numbers
• 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
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Rounding off Numbers – Examples
• 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
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Powers-of-10 Notation (Scientific Notation)
• 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 = 10x10x10x10x10x10 = 106
Section 1.7
11,000 ,000
1
106 = = 0.000001 = 10-6
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Examples of Numbers Expressed in Powers-of-10 Notation
Section 1.7
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Scientific Notation
• 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
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• 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
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• 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
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• 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
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• 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
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• 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
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• 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
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• 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: c = 2πr (π = 3.14159…)
Section 1.7
Problem Example
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• Circumference = c = 2π r (π = 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
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Equation at the end of the chapter with which the student needs to be
familiar• Density: ρ = m/V
Section 1.7