Slide 1AnnouncementsSpecial Problems for Extra CreditDimension and Dimensional AnalysisDimension and Dimensional AnalysisExamplesSome FundamentalsSome More FundamentalsDisplacement, Velocity and SpeedSlide 10Displacement, Velocity and SpeedDifference between Speed and VelocityExample 2.1Instantaneous Velocity and SpeedSlide 15Position vs Time PlotSlide 17Example 2.3Example 2.3 cont’dDisplacement, Velocity and SpeedAccelerationAcceleration vs Time PlotExample 2.4Few Confusing Things on AccelerationDisplacement, Velocity, Speed & AccelerationOne Dimensional MotionSlide 27Slide 28Example 2.11Tuesday, June 7, 2011 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu1PHYS 1443 – Section 001Lecture #2Tuesday, June 7, 2011Dr. Jaehoon Yu•Dimensional Analysis•Fundamentals•One Dimensional Motion: Average Velocity; Acceleration; Motion under constant acceleration; Free FallTuesday, June 7, 2011 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu2Announcements•Homework registration and submissions–18/27 registered but only 1 submitted the answer!–I will then have to approve your enrollment request•So please go ahead and take an action as soon as possible•The roster closes tomorrow, Wednesday!•Quiz tomorrow at the beginning of the class!–Problems will be on Appendices A and B!Tuesday, June 7, 2011 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu3Special Problems for Extra Credit•Derive the quadratic equation for Bx2-Cx+A=0 5 points•Derive the kinematic equation from first principles and the known kinematic equations 10 points•You must show your work in detail to obtain full credit•Due at the start of the class, Thursday, June 9 ifxfxxavvxxi 222Tuesday, June 7, 2011 44Dimension and Dimensional Analysis•An extremely useful concept in solving physical problems•Good to write physical laws in mathematical expressions•No matter what units are used the base quantities are the same–Length (distance) is length whether meter or inch is used to express the size: Usually denoted as [L]–The same is true for Mass ([M])and Time ([T])–One can say “Dimension of Length, Mass or Time”–Dimensions are treated as algebraic quantities: Can perform two algebraic operations; multiplication or divisionPHYS 1443-001, Spring 2011 Dr. Jaehoon YuTuesday, June 7, 2011 55Dimension and Dimensional Analysis•One can use dimensions only to check the validity of one’s expression: Dimensional analysis–Eg: Speed [v] = [L]/[T]=[L][T-1]•Distance (L) traveled by a car running at the speed V in time T–L = V*T = [L/T]*[T]=[L]•More general expression of dimensional analysis is using exponents: eg. [v]=[LnTm] =[L][T-1] where n = 1 and m = -1PHYS 1443-001, Spring 2011 Dr. Jaehoon YuTuesday, June 7, 2011 66Examples•Show that the expression [v] = [at] is dimensionally correct•Speed: [v] =[L]/[T]•Acceleration: [a] =[L]/[T]2•Thus, [at] = (L/T2)xT=LT(-2+1) =LT-1 =[L]/[T]= [v]2 m- =-mnvkra DimensionlessconstantLengthSpeed1 2LT-=rvvkra221r van m+ =•Suppose the acceleration a of a circularly moving particle with speed v and radius r is proportional to rn and vm. What are n andm?( )mnLLT� �=� �� �n m mL T+ - � =m 22n + = 1 � =-n 1PHYS 1443-001, Spring 2011 Dr. Jaehoon YuTuesday, June 7, 2011 77Some Fundamentals•Kinematics: Description of Motion without understanding the cause of the motion•Dynamics: Description of motion accompanied with understanding the cause of the motion•Vector and Scalar quantities:–Scalar: Physical quantities that require magnitude but no direction •Speed, length, mass, height, volume, area, energy, heat, etc–Vector: Physical quantities that require both magnitude and direction•Velocity, Acceleration, Force, Momentum•It does not make sense to say “I ran with velocity of 10miles/hour.”•Objects can be treated as point-like if their sizes are smaller than the scale in the problem–Earth can be treated as a point like object (or a particle) in celestial problems•Simplification of the problem (The first step in setting up to solve a problem…)–Any other examples?PHYS 1443-001, Spring 2011 Dr. Jaehoon YuTuesday, June 7, 2011 88Some More Fundamentals•Motions:Can be described as long as the position is known at any given time (or position is expressed as a function of time)–Translation: Linear motion along a line–Rotation: Circular or elliptical motion–Vibration: Oscillation•Dimensions–0 dimension: A point–1 dimension: Linear drag of a point, resulting in a line Motion in one-dimension is a motion on a line–2 dimension: Linear drag of a line resulting in a surface–3 dimension: Perpendicular Linear drag of a surface, resulting in a stereo objectPHYS 1443-001, Spring 2011 Dr. Jaehoon YuTuesday, June 7, 2011 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu9Displacement, Velocity and SpeedOne dimensional displacement is defined as: ixxxfThe average velocity is defined as: xv �The average speed is defined as: Total Distance TraveledTotal Elapsed Timev �ffiix xt t-=-xtDDDisplacement per unit time in the period throughout the motionDisplacement is the difference between initial and final potions of the motion and is a vector quantity. How is this different than distance?DisplacementElapsed Time�Unit?m/sUnit?mUnit?m/sA vector quantityA scalar quantityA vector quantityTuesday, June 7, 2011 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu10How much is the elapsed time?t=Dt0- t1x2xWhat is the displacement?=xD x21- xTuesday, June 7, 2011 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu11Displacement, Velocity and SpeedOne dimensional displacement is defined as: ixxxfThe average velocity is defined as: xv �The average speed is defined as: Total Distance TraveledTotal Elapsed Timev �Can someone tell me what the difference between speed and velocity is?ffiix xt t-=-xtDDDisplacement per unit time in the period throughout the motionDisplacement is the difference between initial and final potions of the motion and is a vector quantity. How is this different than distance?DisplacementElapsed Time�Unit?m/sUnit?mUnit?m/sTuesday, June 7, 2011 1212Difference between Speed and Velocity•Let’s take a simple one dimensional translation that has many steps:Let’s call this line as X-axisLet’s have a couple of motions in a total time interval of 20 sec.+10m+15m-15m-5m -10m+5mTotal Displacement:xDTotal Distance Traveled:D =Average Velocity:ffixix xvt t-�-Average Speed:Total Distance
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