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A small mass slides down an inclined plane of inclination ‘s’ with horizontal.The coefficient of friction ‘D’ =D 0 x where x is the distance through which the mass slides down and D 0 is a positive constant.find the distance covered by the mass before it comes to rest.
Net Force = mgsin(s) – Dmgcos(s)Net acceleration = gsin(s) – D0xgcos(s)a = vdv/dx = gsin(s) – D0xgcos(s) vdv = gsin(s)dx – D0xgcos(s)dxIntegerating botth sides and with limit of v 0to 0.v^2/2 = xgsin(s) – D0x^2gcos(s)/2 xgsin(s) – D0x^2gcos(s)/2 = 0Hence, x = (2/Do)(sins/cos(s)) = > (2tan(s))/Do m.
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