### An inclined plane is used to measure the coefficient of friction.

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Teachable Topics:

• mechanics
• friction
• Statics

Theory:

If an object is at rest on a surface and you push against it and it doesn't move, are there friction forces acting upon 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 sin(q)., and Newton's laws give us that...

The sum of all the forces in the x-direction is zero:

SFx = fs - mg sin(q) = 0

or

msN - mg sin(q) = 0

so...

msN = mg sin(q)

And the sum of all the forces in the y-direction is zero:

SFy = N - mg cos(q) = 0

or

N = mg cos(q).

From the two end equations, we find that

ms = (mg sin(q)/mg cos(q)) = tan(q)

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.

Apparatus:

• Wooden block
• Incline plane equipment Procedure:

• Place the wooden block on the plane surface ad slowly incline the plane in small increments.
• As you are inclining the plane, gently hold the wooden block with your finger tips. This will ensure that the block will not accidentally be shakes and slide prematurely.
• At a certain inclination, the static friction will be overcome by the weight of the wooden block and the block will slide down the incline. The tangent of this angle is equal to the coefficient of static friction for this block and this plane.