Ch. 1: Introduction, Measurement, Estimating. 1. The Nature of Science 2. Models, Theories, & Laws...
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Transcript of Ch. 1: Introduction, Measurement, Estimating. 1. The Nature of Science 2. Models, Theories, & Laws...
Ch. 1: Introduction, Measurement, Estimating
1. The Nature of Science2. Models, Theories, & Laws3. Measurement & Uncertainty Significant Figures4. Units, Standards, & the SI System5. Converting Units6. Order of Magnitude: Rapid Estimating7. Dimensions & Dimensional Analysis
Chapter 1 Outline
Physics: The most basic of all sciences!Physics: The Parent of all sciences!
Physics = The study of the behavior of and the structure of matter and energy and of the interaction between matter and energy.
Sub Areas of PhysicsThis course (Phys. 1408, the Physics of the 16th & 17th Centuries):Motion (MECHANICS) (most of our time!)Fluids & WavesNext course (Phys. 2401, the Physics of 18th & the 19th Centuries):Electricity & magnetismLight & opticsAdvanced courses (Phys. 2402 & others. The Physics of the 20th Century!):Relativity, atomic structure, condensed matter, nuclear physics, .These are the most interesting Physics topics & the topics which are the most relevant to modern technology!
Mechanics: Classical Mechanics
Mechanics: Classical MechanicsClassical Physics: Classical Before the 20th CenturyThe foundation of pure & applied macroscopic physics & engineering!Newtons Laws + Boltzmanns Statistical Mechanics (& Thermodynamics): Describe most of macroscopic world!However, at high speeds (v ~ c) we need Special Relativity: (Early 20th Century: 1905) Ch. 14 of M&TAlso, for small sizes (atomic & smaller) we need Quantum Mechanics: (1900 through ~ 1930) Physics 4307!Classical Mechanics: (17th & 18th Centuries) Still useful today!
- Classical MechanicsThe mechanics in this course is limited to macroscopic objects moving at speeds v much, much smaller than the speed of light c = 3 108 m/s. As long as v
FYI: The Structure of Physics
SUMMARY: THE STRUCTURE OF PHYSICS
Low SpeedHigh Speed
v > atomic size(Newton, Hamilton,(Einstein)
Small sizeQuantum MechanicsRelativistic Quantum
< ~ atomic size(Schrodinger,Mechanics
Atomic PhysicsQuantum Field Theory
(Photons, Weak Nuclear Force)
(Gluons, Quarks, Leptons
Nuclear & Particle PhysicsStrong Nuclear Force)
Mechanics The science of HOW objects move (behave) under given forces. (Usually) Does not deal with the sources of forces. Answers the question: Given the forces, how do objects move?
Physics: General DiscussionThe Goal of Physics (& all of science): To quantitatively and qualitatively describe the world around us.Physics IS NOT merely a collection of facts & formulas!
Physics IS a creative activity!
Physics Observation Explanation.
Physics & Its Relation to Other FieldsThe Parent of all Sciences!The foundation for and is connected to ALL branches of science and engineering.Also useful in everyday life and in MANY professionsChemistryLife Sciences (Medicine also!!)ArchitectureEngineeringVarious technological fields
Physics Principles are used in many practical applications, including construction. Communication between Architects & Engineers is essential if disaster is to be avoided.
Physics is an EXPERIMENTAL science!Experiments & Observations: Important first steps toward scientific theory.It requires imagination to tell what is importantTheories: Created to explain experiments & observations. Will also make predictionsExperiments & Observations: Will tell if predictions are accurate. No theory can be absolutely verifiedBut a theory CAN be proven false!!!The Nature of Science
TheoryQuantitative (mathematical) description of experimental observations.Not just WHAT is observed but WHY it is observed as it is and HOW it works the way it does.
Tests of theories: Experimental observations: More experiments, more observation.Predictions: Made before observations & experiments.
Model, Theory, LawModel: An analogy of a physical phenomenon to something we are familiar with. Theory: More detailed than a model. Puts the model into mathematical language.Law: Concise & general statement about how nature behaves. Must be verified by many, many experiments! Only a few laws.Not comparable to laws of government!
How does a new theory get accepted?Predictions agree better with data than old theoryExplains a greater range of phenomena than old theoryExample: Aristotle believed that objects would return to a state of rest once put in motion.Galileo realized that an object put in motion would stay in motion until some force stopped it.
No measurement is exact; there is always some uncertainty due to limited instrument accuracy and difficulty reading results.The photograph to the left illustrates this it would be difficult to measure the width of this 2 4 to better than a millimeter.Measurement & Uncertainty.Significant Figures
Measurement & UncertaintyPhysics is an EXPERIMENTAL science!Finds relations between physical quantities.Expresses those relations in the language of mathematics. (LAWS & THEORIES)Experiments are NEVER 100% accurate.Always have uncertainty in final result. Experimental error.Common to state this precision (when known).
Consider a simple measurement of the width of a board. Find 23.2 cm.
However, measurement is only accurate to 0.1 cm (estimated).
Write width as (23.2 0.1) cm 0.1 cm Experimental uncertaintyPercent Uncertainty: (0.1/23.2) 100 0.4%
Significant FiguresSignificant figures (sig figs): The number of significant figures is the number of reliably known digits in a number. It is usually possible to tell the number of significant figures by the way the number is written: 23.21 cm has 4 significant figures 0.062 cm has 2 significant figures (initial zeroes dont count) 80 km is ambiguous: it could have 1 or 2 significant figures. If it has 3, it should be written 80.0 km.
Calculations Involving Several NumbersWhen multiplying or dividing numbers: The number of sig figs in the result the same number of sig figs as the number used in the calculation with the fewest sig figs.When adding or subtracting numbers: The answer is no more accurate than the least accurate number used in the calculation.
Example: (Not to scale!)Area of board, dimensions 11.3 cm 6.8 cmArea = (11.3) (6.8) = 76.84 cm211.3 has 3 sig figs , 6.8 has 2 sig figs 76.84 has too many sig figs!Proper number of sig figs in answer = 2 Round off 76.84 & keep only 2 sig figs Reliable answer for area = 77 cm2
Sig FigsGeneral Rule: The final result of a multiplication or division should have only as many sig figs as the number used in the calculation which has the with least number of sig figs.
NOTE!!!! All digits on your calculator are NOT significant!!
Calculators will not give you the right number of significant figures; they usually give too many, but sometimes give too few (especially if there are trailing zeroes after a decimal point).The top calculator shows the result of 2.0 / 3.0.The bottom calculator shows the result of 2.5 x 3.2.
Conceptual Example 1-1: Significant figuresUsing a protractor, you measure an angle of 30. (a) How many significant figures should you quote in this measurement? (b) Use a calculator to find the cosine of the angle you measured.
(a) Precision ~ 1 (not 0.1). So 2 sig figs & angle is 30 (not 30.0).(b) Calculator: cos(30) = 0.866025403. But angle precision is 2 sig figs so answer should also be 2 sig figs. So cos(30) = 0.87
Powers of 10(Scientific Notation)READ Appendices A-2 & A-3Common to express very large or very small numbers using power of 10 notation.Examples:39,600 = 3.96 104 (moved decimal 4 places to left)0.0021 = 2.1 10-3 (moved decimal 3 places to right)PLEASE USE SCIENTIFIC NOTATION!!
Powers of 10(Scientific Notation)PLEASE USE SCIENTIFIC NOTATION!!This is more than a request!! Im making it a requirement!! I want to see powers of 10 notation on exams!! For example:For large numbers, like 39,600, I want to see 3.96 104 & NOT 39,600!! For small numbers, like 0.0021, I want to see 2.1 10-3 & NOT 0.0021!! On the exams, you will lose points if you dont do this!!
Accuracy vs. PrecisionAccuracy is how close a measurement comes to the accepted (true) value.Precision is the repeatability of the measurement using the same instrument & getting the same result!It is possible to be accurate without being precise and to be precise without being accurate!
Units, Standards, SI SystemAll measured physical quantities have units.Units are VITAL in physics!!In this course (and in most of the modern world, except the USA!) we will use (almost) exclusively the SI system of units.SI = Systme International (French)More commonly called the MKS system (meter-kilogram-second) or more simply, the metric system
SI or MKS SystemDefined in terms of standards for length, mass, and time.Length unit: Meter (m) (kilometer = km = 1000 m)Standard Meter.Newest definition in terms of speed of light Length of path traveled by light in vacuum in (1/299,792,458) of a second! Time unit: Second (s)Standard Second.Newest definition time required for 9,192,631,770 oscillations of radiation emitted by cesium atoms!Mass unit: Kilogram (kg)Standard KilogramMass of a specific platinum-iridium alloy cylinder kept at Intl Bureau of Weights & Measures in France
Larger & Smaller Units are Defined from SI standards by Powers of 10 & Greek PrefixesThese are the standard SI prefixes for indicating powers of 10. Many (k, c, m, ) are familiar; Others (Y, Z, E, h, da, a, z, y) are rarely used.__ __ __ __
Typical Lengths (approx.)
Typical Times (approx.)
Typical Masses (approx.)
Units, Standards, and the SI SystemWe will work (almost) exclusively in the SI System, where the basic units are kilograms, meters, & seconds.
Other Systems of UnitsCGS (centimeter-gram-second) systemCentimeter = 0.01 meterGram = 0.001 kilogramBritish (Engineering) System (foot-pound-second; or US Customary system)Everyday life system of unitsOnly used by USA & some third world countries. Rest of world(including Britain!) uses SI system. We will not use the British System!Conversions exist between the British & SI systems. We will not use them in this course!
In this class, we will NOT do unit conversions!
We will work exclusively in SI (MKS) units!
Basic & Derived QuantitiesBasic Quantity Must be defined in terms of a standard (meter, kilogram, second).
Derived Quantity Defined in terms of combinations of basic quantitiesUnit of speed (v = distance/time) = meter/second = m/sUnit of density ( = m/V) = kg/m3
Units and EquationsIn dealing with equations, remember that the units must be the same on both sides of an equation (otherwise, it is not an equation)!Example: You go 90 km/hr for 40 minutes. How far did you go?
Units and EquationsIn dealing with equations, remember that the units must be the same on both sides of an equation (otherwise, it is not an equation)!Example: You go 90 km/hr for 40 minutes. How far did you go? Equation from Ch. 2: x = vt, v = 90 km/hr, t = 40 min. To use this equation, first convert t to hours: t = ()hr so,x = (90 km/hr) [()hr] = 60 km The hour unit (hr) has (literally) cancelled out in the numerator & denominator!
Converting UnitsAs in the example, units in the numerator & the denominator can cancel out (as in algebra)Illustration: Convert 80 km/hr to m/s Conversions: 1 km = 1000 m; 1hr = 3600 s
Converting UnitsAs in the example, units in the numerator & the denominator can cancel out (as in algebra)Illustration: Convert 80 km/hr to m/s Conversions: 1 km = 1000 m; 1hr = 3600 s 80 km/hr =(80 km/hr) (1000 m/km) (1hr/3600 s)(Cancel units!) 80 km/hr 22 m/s (22.222m/s)Useful conversions: 1 m/s 3.6 km/hr; 1 km/hr (1/3.6) m/s
Order of Magnitude; Rapid EstimatingSometimes, we are interested in only an approximate value for a quantity. We are interested in obtaining rough or order of magnitude estimates.
Order of magnitude estimates: Made by rounding off all numbers in a calculation to 1 sig fig, along with power of 10.Can be accurate to within a factor of 10 (often better)
Example: V = r2d
Example: Estimate!Estimate how much water there is in a particular lake, which is roughly circular, about 1 km across, & you guess it has an average depth of about 10 m.
Example 1-6: Thickness of a page.Estimate the thickness of a page of your textbook. Hint: You dont need one of these!
Example 1-7: Height by triangulation.Estimate the height of the building shown by triangulation, with the help of a bus-stop pole and a friend. (See how useful the diagram is!)
Example 1-8: Estimate the Earth radius.If you have ever been on the shore of a large lake, you may have noticed that you cannot see the beaches, piers, or rocks at water level across the lake on the opposite shore. The lake seems to bulge out between you and the opposite shorea good clue that the Earth is round. Suppose you climb a stepladder and discover that when your eyes are 10 ft (3.0 m) above the water, you can just see the rocks at water level on the opposite shore. On a map, you estimate the distance to the opposite shore as d 6.1 km. Use h = 3.0 m to estimate the radius R of the Earth.
Dimensions & Dimensional AnalysisThe dimensions of a quantity are the base units that make it up; generally written using square brackets.Example: Speed = distance/timeDimensions of speed: [L/T]Quantities that are being added or subtracted must have the same dimensions. In addition, a quantity calculated as the solution to a problem should have the correct dimensions.
Dimensional AnalysisIf the formula for a physical quantity is known The correct units can easily be found! Examples: Volume: V = L3 Volume unit = m3 Cube with L =1 mm V = 1 mm3 = 10-9 m3 Density: = m/V Density unit = kg/m3 = 5.3 kg/m3 = 5.3 10-6 g/mm3 If the units of a physical quantity are known The correct formula can be guessed!Examples: Velocity: Car velocity is 60 km/h Velocity unit = km/h Formula: v = d/t (d = distance, t = time) Acceleration: Car acceleration is 5 m/s2 Acceleration unit = m/s2 Formula: a = v/t (v = velocity, t = time)
Dimensional analysis is the checking of dimensions of all quantities in an equation to ensure that those which are added, subtracted, or equated have the same dimensions.Example: Is this the correct equation for velocity?Check the dimensions: Wrong!
Summary, Ch. 11. Physics = Measurements (Units) + Mathematics (Algebra, Trig, Calculus) + Physical Principles (discussed as we go) + Common Sense!2. SI (mks) system of units: Basic Units: Length m, Time s, Mass kgUnit conversions: 1000m = 1 km, 10-3 kg = 1g, . Derived units: = m/V Density unit = kg/m3 3. Dimensional Analysis If the formula for a physical quantity is known The correct units can be found! If the units of a physical quantity are known The correct formula can be guessed!
4. Theories are created to explain observations, & then tested based on their predictions. 5. A model is like an analogy; it is not intended to be a true picture, but to provide a familiar way of envisioning a quantity.6. A theory is much more well developed than a model, & can make testable predictions; a law is a theory that can be explained simply, & that is widely applicable.7. Measurements can never be exact; there is always some uncertainty. It is important to write them, as well as other quantities, with the correct number of significant figures.8. When converting units, check dimensions to see that the conversion has been done properly.9. Order-of-magnitude estimates can be very helpful
Comparison of 3 Fields of Study
Figure 1-1. Caption: (a) This Roman aqueduct was built 2000 years ago and still stands. (b) The Hartford Civic Center collapsed in 1978, just two years after it was built.Figure 1-8. Caption: Example 16. Micrometer used for measuring small thicknesses.Answer: Measure the thickness of 100 pages. You should find that the thickness of a single page is about 6 x 10-2 mm.Figure 1-9. Caption: Example 17. Diagrams are really useful!Answer: The building is about 15 m tall.
Figure 1-10. Caption: Example 18, but not to scale. You can see small rocks at water level on the opposite shore of a lake 6.1 km wide if you stand on a stepladder.Answer: This calculation gives the radius of the Earth as 6200 km (precise measurements give 6380 km).