Question

why friction does not depend on amount of surface area in contact

Answer 1

Answer:

Friction is a contact force when two surfaces interact. Notice that both of these friction formulas only depend on the coefficient of friction and the normal force. It does not depend the area of contact; it doesn't depend on the sliding speed.

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Answer 2

Answer:

the force due to friction independent of the contact area between two surfaces when the surface area gets too small at that position fiction may be increased because it is maybe also increase into dig surface.