╨╧рб▒с>■  $&■   #                                                                                                                                                                                                                                                                                                                                                                                                                                                ье┴ ┐я jbjbjкjк Ъ╚╚я      ]ввввввв╥╥╥╥╥ ▐ ╥╬ъЎЎЎЎЎЎЎЎЛНННННН,╕Їм─╣вЎЎЎЎЎ╣ВввЎЎЎВВВЎjвЎвЎЛ╢─ввввЎЛВЦВkввЛъ Y;└╢╥╥`"ГFree Body Analysis of the Angle of Repose Place a coin on the cover of either a binder or your textbook. Slowly raise the cover of the textbook, while observing the motionless coin. Eventually, you reach will an angle where the coin breaks free and starts sliding down the slope of the binder. This is the phenomenon we will be analyzing today. Observe the coin on the binder. Before the coin slides, what kind of friction holds it in place? Sketch what a microscopic view of the coin and binder interacting surfaces might look like. Continue tilting the binder until the coin starts sliding. What is the name of the new kind of friction after the coin is moving and how is this different? How would you sketch change? Try to determine the angle at which the coin exactly breaks free. This is known as the Angle of Repose for an object on a slope. What is the Angle of Repose you measure for your coin and the binder or book? (Average 5 repetitions.) Draw a free body diagram of the inclined plane and the coin. Choose coordinate axes so that the normal force is +y-hat and uphill is +x-hat. Identify and label the following forces on the coin: Normal force (FN), Friction (fs = (s FN), and Weight (W = m g). Write Newton's Second Law of motion for any object in equilibrium. What can we mathematically state about objects in equilibrium? Is the coin is equilibrium at the Angle of Repose? Before and after? Explain. We will use N2x and N2y. What calculations must be done to the three forces you have drawn? Which forces do not require such calculations? Write component expressions for N2x and N2y. What do they mean (in words)? Rearrange your equations to solve for FN and fs alone. What do these expressions mean (in words)? Calculate the division: N2x / N2y. Using the identity: tan ( = (sin () / (cos () to simplify your answer. What does this mean about the role of an object's mass with regard to the Angle of Repose and the coefficient of static friction? What are the units of the coefficient of static friction? Does this make sense? What do you calculate as your coefficient of static friction for the binder and coin? Notable recent UC coin (cupro-nickle) masses: Mdime = 2.264g; Mpenny = 3.110g; Mnickel = 4.999g; Mquarter = 5.669 *ШЩзимно░▒ж з н о  ) * 3 4 я ¤√√ў√√√√єєє jqЁ jmЁH*CJ*+]^┘┌─┼╬╧г д 1 2 ~  с т $ % { | я ¤¤¤¤°¤°¤°¤°¤°¤°¤°¤°¤°¤¤ & F*+]^┘┌─┼╬╧г д 1 2 ~  с т $ % { | я №ЎЁъф▐╪╥╠                         ░╨/ ░р=!░"░#Ра$Ра%░|,, ┘№  Г c yg(№,,╪(d'`Р [4@ё 4NormalCJOJPJQJmH <A@Є б<Default Paragraph Fontя   яя я я жимо/2Фал░╗┴╠╙▐цёймё  Daniel L. MacIsaac:Hummel 10GB:Temporary Items:AutoRecovery save of Document1Daniel L. MacIsaacCHummel 10GB: CrsesFall2000:PHY111:Free Body Analysis of the AngleDaniel L. MacIsaacFHummel 10GB: CrsesFall2000:PHY111:WBs:Free Body Analysis of the AngleDaniel L. MacIsaac5Hummel 10GB: CrsesSpr2001:PHY111:WB Angle of repose          ДhДШ■╞ho(.       @Акк└]ххкк8яP@GРTimes New Roman5РАSymbol3Р Arial3РTimes"pН╨hx╥R&x╥R&x╥R&!е└┤┤А>0dя├  )Free Body Analysis of the Angle of ReposeDaniel L. MacIsaacDaniel L. MacIsaac■  рЕЯЄ∙OhлС+'│┘0дРШ╠╪Ї ,8 T ` l xДМФЬ'*Free Body Analysis of the Angle of ReposerdreeDaniel L. MacIsaacoaniNormalLDaniel L. MacIsaaco2niMicrosoft Word 8.0o@@Р╜■а└@Р╜■а└@Р╜■а└■  ╒═╒Ь.УЧ+,∙о0( hpФЬдм ┤╝─╠ ╘ 'Northern Arizona Universityм *Free Body Analysis of the Angle of Repose Title ■    ■   ■    !"■   ¤   %■   ■   ■                                                                                                                                                                                                                                                                                                                                                                   Root Entry         └FА:Xt┌Я└'А1Table             WordDocument        ЪSummaryInformation(    DocumentSummaryInformation8            CompObj    XObjectPool            А:Xt┌Я└А:Xt┌Я└            ■                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           ■      └FMicrosoft Word Document■   NB6WWord.Document.8