A particle of mass M moves along a horizontal x axis from x = 0 to x = L. The coefficient of kinetic friction varies as a function of x as μk(x) = μ0 − αx, where μ0, α are constants of appropriate dim

Question

A particle of mass M moves along a horizontal x axis from x = 0 to x = L. The coefficient of kinetic friction varies as a function of x as μk(x) = μ0 − αx, where μ0, α are constants of appropriate dimensions, so that μk(L) = 0. The total work done by the frictional force during the motion is ημ0MgL,

Accepted Answer

Answer: 1/2 — μk = μ0 − αx μ0 − αL = 0 ⇒ α = μ0/L W.D. by kinetic friction = ∫ fk dx cos180° = ∫₀ᴸ μkmgdx(−1) = −∫₀ᴸ(μ0 − αx)mgdx = −[μ0mgL − αmgL²/2] = −[μ0mgL − (μ0/L)mgL²/2] = −μ0mgL/2 On comparing magnitude wit

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