Physics 207: Lecture 8, Pg 1Physics 207, Physics 207, Lecture 8, SeptLecture 8, Sept 30 30 ‘‘0909Exam 1 ReviewExam 1 ReviewAssignments:Assignments:Practice problems on Kinematics on MPPractice problems on Kinematics on MPExam Thurs Oct 1 5:45 - 7:00 125 Agriculture HallExam Thurs Oct 1 5:45 - 7:00 125 Agriculture Hall Chapters 1, 2, 3, 4.1 - 4.2, 5, 6 Chapters 1, 2, 3, 4.1 - 4.2, 5, 6 Lectures, discussion, labs, HW Lectures, discussion, labs, HW Monday: ReadMonday: Read 4.5,4.6, 8.2, 8.3, 9.1, 9.2 Next week’s lab:Equilibrium Force (M-2) & Circular Motion (M-6)“One had to cram all this stuff into one's mind for the examinations, whetherone liked it or not. This coercion had such a deterring effect on me that, afterI had passed the final examination, I found the consideration of any scientificproblems distasteful to me for an entire year." A. Einstein, about his university education.Physics 207: Lecture 8, Pg 3ReviewReview for Exam 1for Exam 1Ch 1 Concepts of MotionCh 2 Kinematics in 1DCh 3 VectorsCh 4 Kinematics in 2 D (4.1, 4.2 only)Ch 5 Dynamics in 1-DCh 6 Newton’s Laws 1 and 2, friction, tensionLabsError analysisPhysics 207: Lecture 8, Pg 4Physics 207: Lecture 8, Pg 5Physics 207: Lecture 8, Pg 6Physics 207: Lecture 8, Pg 7Physics 207: Lecture 8, Pg 8 Sir Isaac Newton1642-1727Physics 207: Lecture 8, Pg 9Recall - Dynamics Problem-solving StrategyRecall - Dynamics Problem-solving Strategy Model Make simplifying assumptions Visualize Translate words into symbols Draw a sketch Identify forces Draw a free-body diagram Solve Use Newton’s 2nd law Use kinematics to find velocities and positions Assess Does the result make sense? ! r F net= "ir F i= mr aPhysics 207: Lecture 8, Pg 12Physics 207: Lecture 8, Pg 13Physics 207: Lecture 8, Pg 14Physics 207: Lecture 8, Pg 15Suppose you want to compute the kinetic energy of a football thrown by Bret Favre. You measure the mass, m, of the football on a two-pan balance in the lab and determine that the mean mass is 0.40 kg with a standard deviation of 0.02 kg. You measure the speed, s, of the football (measured off your TV screen in instant replay mode) multiple times and record the values given in the table below: Measurement # Speed (m/s) 1 36 2 36 3 35 4 37 5 35 6 37 7 34 8 38 9 36 Assume that each measurement is independent and distributed according to a Gaussian distribution. a.) What is your best estimate of the speed of the football and its standard deviation? ! vbest= v =1Nvi= 36 m/s1N"#=1N $ 1(vi$ v )21N"= 1.2 m/sNote that the standard deviation of the mean = #N= 0.40 m/s What about significant figures? Well, our error calculation tells us that after multiple measurements we know the speed e ven better than we k now it from any single measurement. So it shouldn’t be surprising that the number of significant figures for the speed will increase: The answer is Vbest = 36.00 +/- 0.40 m/sPhysics 207: Lecture 8, Pg 16 Next week… b.) Based on these measurements, what is your best estimate of the kinetic energy of the ball and the your uncertainty in the estimate? Kinetic energy = ! 12mv2 . We will talk about it in a few weeks. ! Kbest=12m v 2= 260 Joules (you'll see this soon)"KK="mm # $ % & ' ( 2+ 2"vv # $ % & ' ( 2 (p. 12 and 13 lab manual)where m = 0.40 kg, "m = 0.02 kg, v = 36.00 m/s and "v = 0.40 m/sso "K/K = 0.055So, K = 260 + / - 14 m/s (keeping track of significant figures)Physics 207: Lecture 8, Pg 19Error Propagation:Error Propagation:Sums and Differences (contSums and Differences (cont’’d)d) Pessimistic:add or subtract absolute(or fractional) errors Optimistic:if the errors are independent andrandom…..! z = x + y "z = "x +"y! "z = "x2+ "y2Physics 207: Lecture 8, Pg 20Error PropagationError PropagationProducts and QuotientsProducts and Quotients Pessimistic: add the fr action al errors Optimistic: if errors are independent and random…! z = xy "zz="xx+"yy! "zz="xx( )2+"yy# $ % & ' ( 2Physics 207: Lecture 8, Pg 21Weight and GravityWeight and Gravity Draw a free-body diagram for: 1. An object falling toward the earth 2. An object at rest on the tableAre both of these accelerating?A. YesB.
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