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Explain whya cyclist bends while negotiating a curve road? |
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Answer» Solution :Let usconsidera cyclistnegotatingacircularlevelroad( notbankedof radiusrwitha speedv.The cycleand thesystemis Cand itgoesin acircleofradiusr withcenteratO / Letuschoosethe lineOCas X-axisand theverticallinethroughO as Z- axisas showninfigure Thesystemas aframeis rotatingaboutZ - axisthe systemis at restin thisrotatingframe.TOsolveproblemsinrotatingframeor reference, wehaveto applya centrifugal force ( pseudoforce) on thesystemwhichwill be`( mv^2 )/(r ) `thisforcewill actthroughthe centrerof gravity .Theforcesactingon thesystemare,(i )gravitationalforce(mg ), (ii ) normalforce (N ) , (iii )frictionalforce(f )and(iv )Centrifugal force`((mv^2)/(r ))` . Asthesystemis in equilibriumin therotationalframeofreference , the n E texternalforceand n e texternaltorque mustbe zero. Let usconsideralltorques aboutthe pointA infigure . Forrotationalequilibrium, ` VEC(tau)_(n e t) =0` The TORQUE DUE tothe gravitionalforceaboutaboutpointA is( mg AB )whichcausesaclockwiseturnthat istakenas negative. Thetorquedueto thecentripetalforceis `((mv^2)/(r) B C)` whichcausesan anticlockwiseturnthatis takenas positive . `- mgAB + (mv^2)/(r)B C=0` `mg AB= (mv^2 )/(r )BC ` from` Delta ABC ,` `AB = ACsin thetaandBC = ACcos theta ` ` Mg AC sin theta= ( mv^2 )/(r )ACcos theta ` ` tan theta = (v^2)/(rg ) ` ` theta = tan^(-1)((v^2)/(rg ))`  
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