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prove that a tangent angle is equal to coeficient kinetic friction when the block slides down the incline?
with a constant speed. (By using Symbols). And if an angle is the max. angle of incline just before the block moves, what is the coeficient kinetic friction in terms of angles?
Fg = Wsinθ
Ff = μWcosθ
If the block is not accelerating,
Ff = Fg
μWcosθ = Wsinθ
μ = tanθ
The second part of your question deals with static friction, not kinetic, and the angle will be larger just before the block moves than it must be after the block starts moving. The coefficient of kinetic friction cannot be given solely in terms of angle in this case.