ME 211 Homework 2 Solutions

ME 211 Homework 2 Solutions

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Unformatted text preview: weightwillbepulledoppositeand paralleltotheforceoffriction,sothemanshouldbeabletoliftmoreweight.Write thetwoequilibriumequationsinthexandy. F F x y W + 0.6N 3 Answers = 0 = N - 200 =0=- W = 360lbs Problem#74.65 ThehomogeneoussemicylinderhasamassmandmasscenteratG.Determinethe largestangleoftheinclinedplaneuponwhichitrestssothatitdoesnotslipdown theplane.Thecoefficientofstaticfrictionbetweentheplaneandthecylinderis s=0.3.Also,whatistheangleforthiscase? 1.) DrawtheFBD 2.)Writetheequilibriumequationsincludingtheforceoffriction.Tobegin,findthe weightinthexdirectionalongtheinclineandtheyperpendiculartotheincline.Your newaxeswillhavexalongtheinclinedsurfaceandywillbeperpendiculartothat. Frition = N W x :W sin( ) W y :W cos( ) 3.)Nowwritetheequilibriumequations.Sumtheforcesalongtheincline,and sumtheforcesperpendiculartotheincline. F F x y = 0 = -W sin( ) + N = 0 = W cos( ) + N 4.)Youwillnoticethatwehavethreeunknowns,(W,N,and),soweneedto eliminateonetohavetwoequations,andtwounknownstoallowustosolvefor . F F x y = 0 = -W sin( ) + N = 0 = -W cos( ) + N N = W cos( ) 0 = -W sin( ) + (W cos( )) W sin( ) = (W cos( )) sin( ) = cos( ) sin( ) = cos( ) tan( ) = = 16.69 Part(b) 4r r = 3 sin(180 - ) sin(16.7) sin = 0.6771 = 42.6 Problem#84.67 A35kgdiskrestsonaninclinedsurfaceforwhichs=0.2.Determinethemaximum verticalforcePthatmaybeappliedtolinkABwithoutcausingthedisktoslipatC. Part(a) 1.)DrawtheFBD 2.Writetheequilibriumequations F = 0 = A - B F = 0 = -P + A + B M = 0 = P(0.6) - A (0.9) x y x x y y B y Ay = 0.667P Part(b) 1.)DrawtheFBD 2.)Writetheequilibriumequations F = 0 = N sin(60) - A - W - N sin(30) M = 0 = N(0.200) - Ay(0.200) M = 0 = N(0.200) - (0.667P)(0.200) y y O O P= N * .667 N * ) - 35 * 9.81- N sin(30) 0.667 0 = N sin(60) - 0.667( N = 606.6N P = 181.9N F F x y = 0 = -W sin( ) + N = 0 = -W cos( ) + N N = W cos( ) 0 = -W sin( ) + (W cos( )) W sin( ) = (W cos( )) sin( ) = cos( ) sin( ) = cos( ) tan( ) = = 16.69...
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This note was uploaded on 05/12/2010 for the course MECHENG 211 taught by Professor ? during the Fall '07 term at University of Michigan.

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