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UW-Madison PHYSICS 207 - Physics 207 – Lecture 2

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Page 1Physics 207 – Lecture 2Physics 207: Lecture 2, Pg 1Lecture 2GoalsGoals: (Highlights of Chaps. 1 & 2.1-2.4)v Conduct order of magnitude calculations, v Determine units, scales, significant digits (in discussion or on your own)v Distinguish between Position & Displacementv Define Velocity (Average and Instantaneous), Speedv Define Accelerationv Understand algebraically, through vectors, and graphically the relationships between position, velocity and accelerationv PerformDimensional AnalysisDimensional AnalysisPhysics 207: Lecture 2, Pg 2Reading QuizDisplacement, position, velocity & acceleration are the main quantities that we will discuss today.Which of these 4 quantities have the same unitsA. Velocity & positionB. Velocity & accelerationC. Acceleration & displacementD. Position & displacementE. Position & accelerationPage 2Physics 207 – Lecture 2Physics 207: Lecture 2, Pg 3Perspective Length/Time/Mass Distance 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 10-15Universal standard: The speed of light is defined to be exactly299 792 458 m/s and so one measures how far light travels in 1/299 792 458 of a second Physics 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 10-24World’s most accurate timepiece: Cesium fountain Atomic ClockLose or gain one second in some 138 million yearsPage 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 7Densityl 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 Densityl 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 molel 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? l Need to know something from your experience:v Average length of french fry: 3 inches or 8 cm, 0.08 mv Earth to moon distance: 250,000 milesv In meters: 1.6 x 2.5 X 105 km = 4 X 108 m v 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 unitsl Useful Conversion factors:v 1 inch = 2.54 cmv 1 m = 3.28 ft v 1 mile = 5280 ft v 1 mile = 1.61 kml 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 unitsl 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 12l This is a very important tool to check your workv Provides a reality check (if dimensional analysis fails then there is no sense in putting in numbers)l 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 Tl 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 Analysisl The force (F) to keep an object moving in a circle can be described in terms of: v velocity (v, dimension L / T) of the objectv mass (m, dimension M)v 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 14Exercise 1Dimensional AnalysisWhich of the following formulas for F could be correct ?A. B. C. RmvF2=2=RvmFF = mvRNote: Force has dimensions of ML/T2Velocity (Velocity (νν, , dimension L / T)dimension L / T)Mass (Mass (mm, dimension M), dimension M)Radius of the circle (Radius of the circle (RR, , dimension L)dimension L)Page 8Physics 207 – Lecture 2Physics 207: Lecture 2, Pg 15Significant Figuresl The number of digits that have merit in a measurement or calculation. l When writing a number, all non-zero digits are significant.l Zeros may or may not be significant.v those used to position the decimal point are not significant (unless followed by a decimal point)v those used to position powers of ten ordinals may or may not be significant.l In


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UW-Madison PHYSICS 207 - Physics 207 – Lecture 2

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