Lecture 2Reading QuizPerspective Length/Time/MassTimeOrder 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 AnalysisExercise 1 Dimensional Analysis Which of the following formulas for F could be correct ?Tracking changes in position: VECTORSMotion in One-Dimension (Kinematics) PositionDisplacementAverage Velocity Changes in position vs Changes in timeAverage SpeedExercise 2 Average VelocityAverage Velocity Exercise 3 What is the average velocity in the last second (t = 3 to 4) ?Average Speed Exercise 4 What is the average speed over the first 4 seconds ? 0 m to -2 m to 0 m to 4 m 8 meters totalInstantaneous velocityExercise 5 Instantaneous VelocitySlide 29Key point: position velocityAccelerationConstant AccelerationInstantaneous AccelerationAssignmentPhysics 207: Lecture 2, Pg 1Lecture 2GoalsGoals: (Highlights of Chaps. 1 & 2.1-2.4) Conduct order of magnitude calculations, Determine units, scales, significant digits (in discussion or on your own) 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 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 & accelerationPhysics 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 exactly 299 792 458 m/s and so one measures how far light travels in 1/299 792 458 of a secondPhysics 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 10-24World’s most accurate timepiece: Cesium fountain Atomic ClockLose or gain one second in some 138 million yearsPhysics 207: Lecture 2, Pg 9Order 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 12This is a very important tool to check your work Provides a reality check (if dimensional analysis fails then there is no sense in putting in 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 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 / s2RmvF22RvmF(a(a))(b(b))(c)(c)F = mvRPhysics 207: Lecture 2, Pg 14Exercise 1Dimensional Analysis Which of the following formulas for F could 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 18Tracking changes in position: VECTORSPositionDisplacement (change in position)Velocity (change in position with time)Acceleration (change in velocity with time)Jerk (change in acceleration with time)Be careful, only vectors with identical units can be added/subtractedPhysics 207: Lecture 2, Pg 19Motion in One-Dimension (Kinematics) PositionPosition is usually measured and referenced to an origin: At time= 0 seconds Pat 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 20PatxiDisplacementOne second later Pat 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 meters to the right !t = tf - ti = 1 secondRelating x to t yields velocityxfΔxPhysics 207: Lecture 2, Pg 21Average VelocityChanges in position vs Changes in time ) timetotal()ntdisplacemenet ( velocityaveragetxv•Average velocity = net distance covered per total time, includes BOTH magnitude and direction•Pat’s average velocity was 5 m/s to the right )sec 1()right the tom 5( velocityaveragetxvPhysics 207: Lecture 2, Pg 22Average Speed Speed, s, is usually just the magnitude of velocity. The “how fast” without the direction.However:Average speed
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