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A sphere is rolling without slipping on a rough surface..Is there is arrangement done which can nullify the effect of friction i.e. altough friction is there, no force due to ftiction acts on it while rolling?

A sphere is rolling without slipping on a rough surface..Is there is arrangement done which can nullify the effect of friction i.e. altough friction is there, no force due to ftiction acts on it while rolling?

Grade:Upto college level

1 Answers

vikas askiitian expert
509 Points
10 years ago

consider a sphere rolling on a frictious surface......

A force F is acting on the sphere horizontally ,r distance above the center of sphere....

friction force will be in foreward direction and let it be f  ..

now we have ,

            f + F = ma...........1    (for translational motion)

 and            

 F r- fR = I(angular accleration)     ,                      

(for rolling without slipping,      a=(angular accleration)R)


Fr - fR = Ia/R       (R is radius of sphere and I is moment of inertia of sphere)


  or            Fr - fR= 2MaR/5                       (I for sphere is 2MR2 /5)


  or            F  -  fR/r = 2MaR/5r ............2

  eq 1 - eq 2 


            f(1+R/r) = Ma(1-2R/5r)


            f= Ma(1-2R/5r) /1+R/r   

   

now f = 0 when r =2R/5

 therefore when a force acts on the sphere at a distance 2R/5 above the center then sphere friction force acting on the sphere will be zero.......

 

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