PHYS 1441 – Section 004 Lecture #2AnnouncementsSlide 3UncertaintiesSignificant FiguresSlide 6Needs for Standards and UnitsDefinition of Base UnitsPrefixes, expressions and their meaningsInternational Standard InstitutesHow do we convert quantities from one unit to another?Examples 1.3 & 1.4Estimates & Order-of-Magnitude CalculationsExample 1.5Dimension and Dimensional AnalysisSlide 16ExamplesSome FundamentalsMonday, Jan. 26, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu1PHYS 1441 – Section 004Lecture #2Monday, Jan. 26, 2004Dr. Jaehoon Yu•Chapter one–Uncertainties and Significant Figures–Standards and units–Estimates–Unit conversions•Chapter two–Fundamentals–Velocity and Speed (Average and instantaneous)–AccelerationMonday, Jan. 26, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu2Announcements•Reading assignment #2: Read and follow through Appendix sections by Monday, Feb. 2–A-5, A-6, A-7, A-8 and A-9•There will be a quiz on Wednesday, Jan. 28•Homework Registration: 42/65 (15 of you submitted it)–You mustmust download, print, solve and submit electronically your homework to obtain 100% credit for homework #1–Homework #1 due 1pm, Wednesday, Jan. 28 –Roster will close Wednesday, Jan. 28•E-mail distribution list (phys1441-004-spring04)–18 of you subscribed as of 10am this morning–5 points5 points extra credit if done by 6pm today, Jan. 26–3 points3 points extra credit if done by 6pm Wednesday, Jan. 28–1 point1 point extra credit if done by 6pm Monday, Feb. 2Monday, Jan. 26, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu3Monday, Jan. 26, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu4Uncertainties•Physical measurements have limited precision, however good it is, due to:–Number of measurements –Quality of instruments (meter stick vs micro-meter)–Experience of the person doing measurements–Etc–In many cases, uncertainties are more important and difficult to estimate than the central (or mean) valuesStat.{{Syst.Why and when do uncertainties matter?Monday, Jan. 26, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu5Significant Figures•Significant figures denote the precision of the measured values–Significant figures: non-zero numbers or zeros that are not place-holders•34 has two significant digits, 34.2 has 3, 0.001 has one because the 0’s before 1 are place holders, 34.100 has 5, because the 0’s after 1 indicates that the numbers in these digits are indeed 0’s.•When there are many 0’s, use scientific notation: –31400000=3.14x107–0.00012=1.2x10-4Monday, Jan. 26, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu6Significant Figures•Operational rules:–Addition or subtraction: Keep the smallest number of decimal place in the result, independent of the number of significant digits: 34.001+120.1=154.1–Multiplication or Division: Keep the smallest significant figures in the result: 34.001x120.1 = 4083, because the smallest significant figures is 4.Monday, Jan. 26, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu7Needs for Standards and Units•Basic quantities for physical measurements–Length, Mass, and Time•Need a language that everyone can understand each other–Consistency is crucial for physical measurements–The same quantity measured by one must be comprehendible and reproducible by others–Practical matters contribute•A system of unit called SISI (System Internationale) established in 1960–Length in meters (m)–Mass in kilo-grams (kg)–Time in seconds (s)Monday, Jan. 26, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu8Definition of Base UnitsOne second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the Cesium 133 (C133) atom.1 s (Time)It is equal to the mass of the international prototype of the kilogram, made of platinum-iridium in International Bureau of Weights and Measure in France. 1 kg (Mass) = 1000 gOne meter is the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second.1 m (Length) = 100 cmDefinitionsSI Units•There are prefixes that scales the units larger or smaller for convenience (see pg. 11)•Units for other quantities, such as Kelvins for temperature, for easiness of useMonday, Jan. 26, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu9Prefixes, expressions and their meanings•deci (d): 10-1•centi (c): 10-2•milli (m): 10-3•micro (): 10-6•nano (n): 10-9•pico (p): 10-12•femto (f): 10-15•atto (a): 10-18•deca (da): 101•hecto (h): 102•kilo (k): 103•mega (M): 106•giga (G): 109•tera (T): 1012•peta (P): 1015•exa (E): 1018Monday, Jan. 26, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu10International Standard Institutes•International Bureau of Weights and Measure http://www.bipm.fr/–Base unit definitions: http://www.bipm.fr/enus/3_SI/base_units.html –Unit Conversions: http://www.bipm.fr/enus/3_SI/ •US National Institute of Standards and Technology (NIST) http://www.nist.gov/Monday, Jan. 26, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu11How do we convert quantities from one unit to another?Unit 1 = Unit 2Conversion factor X1 inch 2.54 cm1 inch 0.0254 m1 inch 2.54x10-5km1 ft 30.3 cm1 ft 0.303 M1 ft 3.03x10-4km1 hr 60 minutes1 hr 3600 secondsAnd many More Here….Monday, Jan. 26, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu12Examples 1.3 & 1.4•Ex 1.3: A silicon chip has an area of 1.25in2. Express this in cm2. 21.25 in =22cm 06.8cm 45.6 25.1 222in 1cm 45.6in 25.1•Ex 1.4: Where the posted speed limit is 65 miles per hour (mi/h or mph), what is this speed (a) in meters per second (m/s) and (b) kilometers per hour (km/h)? 1 mi= 65 mi/h =65 mi/h =(a)(b)21.25 in �What do we need to know?22.54 cm1 i n� �� �� �( )5280 ft1609 m 1.609 km =12 in1 ft� �� �� �2.54 cm1 in� �� �� �1 m100cm� �=� �� �( )65 mi29.1 m/s 1609 m1 mi� �� �� �1 1 h� �� �� �1 h3600 s� �=� �� �( )65 mi104 km/h 1.609 km1 mi� �� �� �1 1 h� �=� �� �Monday, Jan. 26, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu13Estimates & Order-of-Magnitude Calculations •Estimate = Approximation–Useful for rough calculations to determine the necessity of higher precision–Usually done under certain assumptions–Might require modification of assumptions, if higher precision is necessary•Order of magnitude
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