physics challenge for teachers and students 2010.pdf

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1、PhysicsChallengeforBorisKorsunsky,ColumnEditorWestonHighSchool,Weston,MA02493TeachersandStudentskorsunbo@post.harvard.eduSolutiontoJanuary2010Challenge◗RiseandshineAlongthinuniformrodliesflatonthetableasshown.TheFsinθforcecausestherod’sbottomendtoslipinOneendoftherodisslowlypulledupbyaforcethato

2、nedirection.Thefrictionforcecountersthisforcetoremainsperpendiculartotherodatalltimes.Whatmini-stoptheslippingwhenFfric=μsNFsinθ.mumcoefficientofstaticfrictionisrequiredsothattheHence,rodcanbebroughttotheverticalpositionwithoutanyslippingofthebottomend?Thegraphofµsshowsthatthevaluesofµsabovethe

3、graphwillpreventtherodfromslipping.Thus,weneedtofindtheµsatitshighestpointwithintherangeofθgiven.Fromthegraphbelow,thereisavalueofθthatcorre-spondstothemaximumvalueofµsneededfortheentirecycleofraisingtherodtoaverticalposition.ThisistheminimumµsneededasifweuseasmallervaluefortheSolution:minimum.G

4、raphofCoefficientofstaticfrictionagainstthetaCoefficientofstaticfrictionf(x)=(cos(x)*sin(x))/(2-(cos(x))^2)thetaπ/50π/253π/502π/25π/103π/257π/504π/259π/50π/511π/506π/2513π/507π/253π/108π/2517π/509π/2519π/502π/521π/5011π/2523π/5012π/25AssumethatMaximumofµscanbefoundbysettingitsderivativewithrespe

5、cttothetaequaltozero:Sincetherodisraisedslowly(quasi-statically),theentiresystemremainsinequilibriumatanymomentintime.Thus,thetorqueaboutthepointofrotationofthe=0rodiszeroaboutanyaxis,andthenetexternalforcesare0.Thedenominatorisalwaysgreaterthan0,soallΘval-Ffric=Fsinθuesarepossible.Letcos2θ=x.He

6、nce,(2-x)(2x-1)–2x(1-x)=0N=mg–Fcosθ1THEPHYSICSTEACHER◆Vol.48,2010FredrickP.Gram(CuyahogaCommunityCollege,Cleve-land,OH)GeraldE.Hite(TAMUG,Galveston,TX)ArtHovey(Milford,CT)J.Iñiguez(UniversidaddeSalamanca,Salamanca,Spain)Per-OlofJansson(Stockholm,Sweden)DavidJones(FloridaInternationalUniversity,M

7、iami,FL)JackKingston(WestonHighSchool,Weston,CT)JeffMelmed(EasternMaineCommunityCollege,Ban-(ContributedbyLohLayKuan,student,NUSHighSchoolgor,ME)ofMathematicsandScience,Singapore)MatthewW.Milligan(FarragutHighSchool,Knoxvill