A Mathematical Model To Analyse The Effects Of Sliding Friction On The Motion Of A Person Sliding Down A Rough Circular Track

The objective of this paper is to analyse the effects of sliding friction on the motion of a Personon a rough vertical circular slide. Aslide which represents a quadrant of radius 5m and a person of mass 60kgis considered for comparison in this paper. A Differential equation for motion is establishedand is solved using integrating factor method andthe motion is analysed for different surface roughness of the slide and is compared using superimposed graphs,also the value of critical coefficient of friction beyond which the person does not exit or come out of the slide is determined.The correction factor for exit velocity with friction is determined. The fraction of energy lost to friction at the exit is evaluated. The Variation of normal force with the position of the person on the slide is plotted for different surface roughnesses of the slide, and the position on the slide where the normal force or the force experienced by the person is maximum, is determined and hence its maximum value is evaluated for different surface roughnesses. For simplicity a point contact between the body and the slide is considered Index terms-critical coefficient of friction, correction factor, exit velocity, integrating factor method, sliding friction,