An inclined plane is used to measure the coefficient of static friction between it and a wooden block.
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If an object is at rest on a surface and you push against it and it doesn't move, is there friction on the object?
The answer is "yes", but this kind of friction is different from kinetic friction. Whereas kinetic friction acts to resist the motion of an object sliding across a surface, static friction is the force which keeps a motionless object from being pushed or pulled across a surface.
If a wooden block is at rest on a horizontal wooden surface, it is acted upon only by the normal force and the gravitational force.
If the surface is inclined so much that the mgsinq component of the object's weight exceeds fs, max, then static friction is overcome, and the block begins to slide. At the angle where the block is just on the verge of slipping, fs max is equal to mg sinq., and Newton's laws give us that...
The sum of all the forces in the x-direction is zero:
SFx = fs - mgsinq = 0
msN - mgsinq = 0
msN = mgsinq.
And the sum of all the forces in the y-direction is zero:
SFy = N - mgcosq = 0
N = mgcosq.
From the two red equations, we find that
ms = (mgsinq/mgcosq) = tanq
So the coeffiecient of static friction is equal to the tangent of the angle of inclination where the block is just on the verge of slipping.