Lecture 2Slide 2LengthTimeOrder of Magnitude Calculations / EstimatesOrder of Magnitude Calculations / Estimates Question: 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?Dimensional Analysis (reality check)Exercise 1 Dimensional AnalysisMoving between pictorial and graphical representationsTracking changes in position: VECTORSMotion in One-Dimension (Kinematics) Position / DisplacementPosition / DisplacementSpeed & Velocity Changes in position vs Changes in timeRepresentative examples of speedInstantaneous velocity Changes in position vs Changes in timeExercise 2 Average VelocityAverage Velocity Exercise 3 What is the average velocity in the last second (t = 3 to 4) ?Exercise 4 Instantaneous VelocityAverage Speed Exercise 5Key point:Motion in Two-Dimensions (Kinematics) Position / DisplacementSlide 22Average AccelerationInstantaneous AccelerationSlide 25Assignment RecapPhysics 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 Perform Dimensional Analysis Dimensional 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)Physics 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 4TimeIntervalInterval Time (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 5Order of Magnitude Calculations / Estimates Question: 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?Physics 207: Lecture 2, Pg 6Order of Magnitude Calculations / Estimates Question: 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 107 secyears 200s/yr103s105 sec. 105.0moon) (to 105.0m 108m 10479101028ffPhysics 207: Lecture 2, Pg 7This 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 TLeft units and right units don’t match, so answer is nonsense units and right units don’t match, so answer is nonsenseDimensional Analysis (reality check)Physics 207: Lecture 2, Pg 8Exercise 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 / s2RmvF22RvmF(a(a))(b(b))(c)(c)F = mvRPhysics 207: Lecture 2, Pg 9Moving between pictorial and graphical representations Example: Initially I walk at a constant speed along a line from left to right, next smoothly slow down somewhat, then smoothly speed up, and, finally walk at the same constant speed.1. Draw a pictorial representation of my motion by using a particle model showing my position at equal time increments.2. Draw a graphical “xy” representation of my motion with time on the x-axis and position along the y-axis. Need to develop quantitative method(s) for algebraically describing: 1. Position2. Rate of change in position (vs. time)3. Rate of change in the change of position (vs. time)Physics 207: Lecture 2, Pg 10Tracking changes in position: VECTORSPositionDisplacement (change in position)Velocity (change in position with time)AccelerationPhysics 207: Lecture 2, Pg 11Motion in One-Dimension (Kinematics) Position / DisplacementPosition is usually measured and referenced to an origin: At time= 0 seconds Joe is 10 meters to the right of the lamp origin = lamp positive direction = to the right of the lamp position vector :10 meters JoeO-x+x10 metersPhysics 207: Lecture 2, Pg 12JoexiPosition / DisplacementOne second later Joe is 15 meters to the right of the lampDisplacement is just change in position.x = xf - xi10 meters15 metersOxf = xi + x x = xf - xi = 5 meterst = tf - ti = 1 secondxfΔxPhysics 207: Lecture 2, Pg 13Speed & VelocityChanges in position vs Changes in time ) timetotal()ntdisplacemenet ( velocityaveragetxvSpeed, Speed, ss, is usually just the magnitude of velocity., is usually just the magnitude of velocity. The “how fast” without the direction.Average speed references the total distance travelledAverage speed references the total distance travelled•Average velocity = net distance covered per total time,Average velocity = net distance covered per total
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