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UW-Madison PHYSICS 207 - Lecture Note

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Page 1Physics 207 – Lecture 2Physics 207: Lecture 2, Pg 1Lecture 2GoalsGoals: (Highlights of Chaps. 1 & 2.1-2.4) Units and scales, order of magnitude calculations, significant digits (on your own for the most part) Distinguish between Position & Displacement Define Velocity (Average and Instantaneous), Speed Define Acceleration Understand algebraically, through vectors, and graphically the relationships between position, velocity and acceleration PerformDimensional AnalysisDimensional AnalysisPhysics 207: Lecture 2, Pg 2Lecture 2Reading Assignment: Reading Assignment: For next class: Finish reading Ch. 2, read For next class: Finish reading Ch. 2, read Chapter 3 (Vectors)Chapter 3 (Vectors)Page 2Physics 207 – Lecture 2Physics 207: Lecture 2, Pg 3LengthDistance Distance Length (m)Length (m)Radius of Visible Universe 1 x 1026To Andromeda Galaxy 2 x 1022To nearest star 4 x 1016Earth to Sun 1.5 x 1011Radius of Earth 6.4 x 106Sears Tower 4.5 x 102Football Field 1 x 102Tall person 2 x 100Thickness of paper 1 x 10-4Wavelength of blue light 4 x 10-7Diameter of hydrogen atom 1 x 10-10Diameter of proton 1 x 10-15See http://micro.magnet.fsu.edu/primer/java/scienceopticsuPhysics 207: Lecture 2, Pg 4TimeIntervalIntervalTime (s)Time (s)Age of Universe 5 x 1017Age of Grand Canyon 3 x 1014Avg age of college student 6.3 x 108One year 3.2 x 107One hour 3.6 x 103Light travel from Earth to Moon 1.3 x 100One cycle of guitar A string 2 x 10-3One cycle of FM radio wave 6 x 10-8One cycle of visible light 1 x 10-15Time for light to cross a proton 1 x 10-24Page 3Physics 207 – Lecture 2Physics 207: Lecture 2, Pg 5MassStuffMass (kg)Mass (kg)Visible universe ~ 1052Milky Way galaxy 7 x 1041Sun 2 x 1030Earth 6 x 1024Boeing 747 4 x 105Car 1 x 103Student 7 x 101Dust particle 1 x 10-9Bacterium 1 x 10-15Proton 2 x 10-27Electron 9 x 10-31Neutrino <1 x 10-36Physics 207: Lecture 2, Pg 6Some Prefixes for Power of TenPowerPowerPrefix Prefix Abbreviation103kilo k106mega M109giga G1012tera T1015peta P1018exa E10-18atto a10-15femto f10-12pico p10-9nano n10-6micro µ10-3milli mPage 4Physics 207 – Lecture 2Physics 207: Lecture 2, Pg 7Density Every substance has a density, designated ρ = M/V• Dimensions of density are, units (kg/m3)3LM≡ρ• Some examples,Substance ρ (103kg/m3)Gold 19.3Lead 11.3Aluminum 2.70Water 1.00Physics 207: Lecture 2, Pg 8Atomic Density In dealing with macroscopic numbers of atoms (and similar small particles) we often use a convenient quantity called Avogadro’s Number, NA= 6.023 x 1023atoms per mole Commonly used mass units in regards to elements 1. Molar Mass = mass in grams of one mole of the substance (averaging over natural isotope occurrences)2. Atomic Mass = mass in u (a.m.u.) of one atom of a substance. It is approximately the total number of protons and neutrons in one atom of that substance. 1u = 1.660 538 7 x 10-27kgatom/mol10023.6g/mol .12 (carbon) 23×=MWhat is the mass of a single carbon (C12) atom ?= 2 x 10-23g/atomPage 5Physics 207 – Lecture 2Physics 207: Lecture 2, Pg 9Order of Magnitude Calculations / EstimatesQuestion: If you were to eat one french fry per second, estimate how many years would it take you to eat a linear chain of trans-fat free french fries, placed end to end, that reach from the Earth to the moon?  Need to know something from your experience: Average length of french fry: 3 inches or 8 cm, 0.08 m Earth to moon distance: 250,000 miles In meters: 1.6 x 2.5 X 105 km = 4 X 108 m  1 yr x 365 d/yr x 24 hr/d x 60 min/hr x 60 s/min = 3 x 107secyears 200s/yr103s105 sec. 105.0moon) (to 105.0m 108m 10479101028=××=××≈××≈−ffPhysics 207: Lecture 2, Pg 10Converting between different systems of units Useful Conversion factors: 1 inch = 2.54 cm 1 m = 3.28 ft  1 mile = 5280 ft  1 mile = 1.61 km Example: Convert miles per hour to meters per second:sm21sm447.0s 3600hr 1ft28.3m 1mift 5280hrmi 1hrmi1 ≈=×××=Page 6Physics 207 – Lecture 2Physics 207: Lecture 2, Pg 11Home Exercise 1Converting between different systems of units When on travel in Europe you rent a small car which consumes 6 liters of gasoline per 100 km. What is the MPG of the car ?(There are 3.8 liters per gallon.)galmi40galmi6.39gal 8.3km 1.6mi 6km 001km6100==××=lllPhysics 207: Lecture 2, Pg 12 This is a very important tool to check your work Provides a reality check (if dimensional analysis fails then no sense in putting in the numbers) ExampleWhen working a problem you get an expression for distance d = v t 2( velocity · time2 )Quantity on left side d L length(also T time and v m/s L / T) Quantity on right side = L / T x T2 = L x T Leftunits and right units donunits and right units don’’t match, so answer is nonsenset match, so answer is nonsenseDimensional Analysis (reality check)Page 7Physics 207 – Lecture 2Physics 207: Lecture 2, Pg 13Exercise 1Dimensional Analysis The force (F) to keep an object moving in a circle can be described in terms of:  velocity (v, dimension L / T) of the object mass (m, dimension M) radius of the circle (R, dimension L)Which of the following formulas for F could be correct ?Note: Force has dimensions of ML/T2 or kg-m / s2RmvF2=2=RvmF(a)(a)(b)(b)(c)(c)F = mvRPhysics 207: Lecture 2, Pg 14Significant Figures The number of digits that have merit in a measurement or calculation.  When writing a number, all non-zero digits are significant. Zeros may or may not be significant. those used to position the decimal point are not significant (unless followed by a decimal point) those used to position powers of ten ordinals may or may not be significant. In scientific notation all digits are significant Examples:2 1 sig fig40 ambiguous, could be 1 or 2 sig figs (use scientific notations)4.0 x 1012 significant figures0.0031 2 significant figures3.03 3 significant figuresPage 8Physics 207 – Lecture 2Physics 207: Lecture 2, Pg 15Significant Figures When multiplying or dividing, the answer should have the same number of significant figures as the least accurate of the quantities in the calculation. When adding or subtracting, the number of digits to the right of the decimal point should equal that of the term in the sum or difference that has the smallest number of digits to the right of the decimal point. Examples: 2 x 3.1 = 6 4.0 x 101/


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UW-Madison PHYSICS 207 - Lecture Note

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