Slide 1Physics 207, Lecture 2, Sept. 10LengthTimeMassSome Prefixes for Power of TenOrder of Magnitude Calculations / Estimates Question: How many french fries, placed end to end, would it take to reach the moon?Dimensional AnalysisLecture 2, Exercise 1 Dimensional AnalysisLecture 2, Exercise 1 Dimensional Analysis Which of the following formulas for F could be correct ?Converting between different systems of unitsLecture 2, Home Exercise 1 Converting between different systems of unitsSignificant FiguresSlide 14Motion in One-Dimension (Kinematics) Position / DisplacementPosition / DisplacementAverage speed and velocity Changes in position vs Changes in timeAverage Velocity Exercise 2 What is the average velocity over the first 4 seconds ?Average Velocity Exercise 3 What is the average velocity in the last second (t = 3 to 4) ?Instantaneous velocity Exercise 4 What is the instantaneous velocity in the last second?Average Speed Exercise 5 What is the average speed over the first 4 seconds ?Key point:Exercise 6, (and some things are easier than they appear)Motion in Two-Dimensions (Kinematics) Position / DisplacementSlide 25Position, velocity & accelerationAnd given a constant acceleration we can integrate to get explicit v and aAssignment RecapPhysics 207: Lecture 2, Pg 1Physics 207 Labs……start this week (MC1a & 1c)Physics 207: Lecture 2, Pg 2Physics 207, Physics 207, Lecture 2, Sept. 10Lecture 2, Sept. 10Agenda for TodayAgenda for TodayFinish Chapter 1, Chapter 2.1, 2.2Finish Chapter 1, Chapter 2.1, 2.2 Units and scales, order of magnitude calculations, significant Units and scales, order of magnitude calculations, significant digits (on your own for the most part)digits (on your own for the most part) Position, DisplacementPosition, Displacement Velocity (Average and Instantaneous), SpeedVelocity (Average and Instantaneous), Speed AccelerationAcceleration Dimensional AnalysisDimensional AnalysisAssignments: Assignments: For next class: Finish reading Ch. 2, read Chapter 3 (Vectors)For next class: Finish reading Ch. 2, read Chapter 3 (Vectors)Mastering Physics: HW1 Set Mastering Physics: HW1 Set due this Wednesday, 9/10due this Wednesday, 9/10Mastering Physics: HW2 available soon, due Wednesday, 9/17Mastering Physics: HW2 available soon, due Wednesday, 9/17(Each assignment will contain, 10 to 11 problems (Each assignment will contain, 10 to 11 problemsPhysics 207: Lecture 2, Pg 3LengthLengthDistanceDistanceLength (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 10-15Physics 207: Lecture 2, Pg 4TimeTimeIntervalIntervalTime (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 10-24Physics 207: Lecture 2, Pg 5MassMassObjectObjectMass (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 TenSome Prefixes for Power of TenPowerPowerPrefix Prefix Abbreviation103 kilo k106 mega M109 giga G1012 tera T1015 peta P1018 exa E10-18 atto a10-15 femto f10-12 pico p10-9 nano n10-6 micro 10-3 milli mPhysics 207: Lecture 2, Pg 7Order of Magnitude Calculations / EstimatesOrder of Magnitude Calculations / Estimates Question: How many french fries, placed end to Question: How many french fries, placed end to end, would it take to reach the moon? end, would it take to reach 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 105.0m 108m 1041028ffPhysics 207: Lecture 2, Pg 8This 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; this leads to the GIGO paradigm)ExampleExampleWhen working a problem you get the answer for distance d = v t 2 ( velocity x time2 )Quantity on left side = LQuantity on right side = L / T x T2 = L x TLeft units and right units don’t match, so answer is Left units and right units don’t match, so answer is nonsensenonsenseDimensional Analysis Dimensional AnalysisPhysics 207: Lecture 2, Pg 9Lecture 2, Lecture 2, Exercise 1Exercise 1Dimensional AnalysisDimensional Analysis The The force (F)force (F) to keep an object moving in a circle can to keep an object moving in a circle can be described in terms of: be described in terms of: velocity (velocity (vv, dimension , dimension L / TL / T) of the object) of the object mass (mass (mm, dimension , dimension MM)) radius of the circle (radius of the circle (RR, dimension, dimension L L))Which of the following formulas for Which of the following formulas for FF couldcould be correct ? be correct ?Note: Force has dimensions of ML/T2RmvF22RvmF(a)(a)(b)(b)(c)(c)F = mvRPhysics 207: Lecture 2, Pg 10 Lecture 2, Lecture 2, Exercise 1Exercise 1Dimensional AnalysisDimensional Analysis Which of the following formulas for Which of the following formulas for FF couldcould be correct ? be correct ? RmvF22RvmFF = mvRNote: Force has dimensions of ML/T2Velocity (Velocity (, , 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)Physics 207: Lecture 2, Pg 11Converting between different systems of unitsConverting between different systems of unitsUseful Conversion factors: 1 inch = 2.54 cm 1 m = 3.28 ft 1 mile = 5280 ft 1 mile = 1.61 kmExample: Convert miles per hour to meters per second:sm21sm447.0s 3600hr 1ft28.3m 1mift 5280hrmi 1hrmi1
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