Physics 207: Lecture 29, Pg 1Physics 207,Physics 207, Lecture 29, DecLecture 29, Dec 14 14 ‘‘0909TODAY: Review!ASSIGNMENTS:ASSIGNMENTS:Practice Problems on MPPractice Problems on MPFINAL EXAM:FINAL EXAM:Bring calculator, equation sheet (8.5Bring calculator, equation sheet (8.5”” x 11 x 11””, 2 sides), 2 sides)Covers entire courseCovers entire course- (but skip 17.6 - (but skip 17.6 ‘‘calorimetrycalorimetry’’ and 17.8and 17.8 ‘‘heat transferheat transfer’’))Consultation hours continue through Tues Dec 22Consultation hours continue through Tues Dec 22Physics 207: Lecture 29, Pg 2TopicsTopicsPhysics 207: Lecture 29, Pg 3StrategyStrategyPhysics 207: Lecture 29, Pg 4Physics 207: Lecture 29, Pg 5Physics 207: Lecture 29, Pg 6Physics 207: Lecture 29, Pg 7Physics 207: Lecture 29, Pg 10Physics 207: Lecture 29, Pg 11Physics 207: Lecture 29, Pg 12Physics 207: Lecture 29, Pg 13Physics 207: Lecture 29, Pg 16Physics 207: Lecture 29, Pg 17Physics 207: Lecture 29, Pg 18Mean and Standard DeviationMean and Standard Deviationofof ‘‘RandomRandom’’ or or ‘‘StatisticalStatistical’’ Errors ErrorsMean =Standard Deviation σ = = 0.179 sWhat is the period of this pendulum?! ="µ="n= 0.09sStandard deviation of the meanStandard errorError in the mean43.60 sOur best estimate of the period is 3.60 +/- 0.09 sPhysics 207: Lecture 29, Pg 19Normal or Gaussian DistributionNormal or Gaussian Distribution For random processes Suppose we make a total of 10 measurements of x, theperiod of the pendulum: 3.9, 3.5, 3.7, 3.4, 3.5, 3.6, 3.7, 3.6, 3.8, 3.6 We plot a histogram of the results:2σ = 0.28Physics 207: Lecture 29, Pg 20Error Propagation:Error Propagation:If the errors are independent and random….. addition and subtraction: multiplication and division:! z = x + y "z = "x2+ "y2! z =xnym...qkrl... "zz= n"xx( )2+ m"yy# $ % & ' ( 2+ k"qq# $ % & ' ( 2+ l"rr( )2 ‘relative error’‘absolute error'Physics 207: Lecture 29, Pg 21Error propagationError propagationYou are trying to compute the density of a sphericalkidney stone. You measure the mass to be 8.0 g andthe radius to be 2.1 mm. Your uncertainty in themeasurements is 0.1 g and 0.1 mm, respectively.What is your best estimate of the density of the stone?! "=mV=m4#r3/ 3= 0.206$""=$mm% & ' ( ) * 2+ 3$rr% & ' ( ) * 2=0.18.0% & ' ( ) * 2+ 30.12.1% & ' ( ) * 2= 0.143$"= 0.143+ 0.206 = 0.0295 = 0.03"= 0.21± 0.03gmm3one sig. figureadjust significant figuresonly good to 2 sig figsonly good to 1 sig
View Full Document
Unlocking...