The coefficient of static friction between two surfaces depends on
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It is independent of area of contact, mass of the objects and practically everything else. But it is constant between two materials. It is a constant on which the magnitude of maximum static frictional force depends.
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The coefficient of static friction depends on External force acting on it.
For an object at rest on a flat table, static friction is zero. ... The maximum static friction force is: (fs)max = μs N where μs is the coefficient of static friction. Static friction is subtle because the static friction force is variable and depends on the external forces acting on an object.
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