[Paul Copioli]

The quantitative (testing) way to determine Mu is by putting the material you want to test on an inclined surface you wnt to test it against. In our csae, this is the carpet. Keep lifting the incline until your material starts to slip. You can calculate Mu by taking the tangent of the angle from horizontal. Mu = tan(theta).

Note that the tan(90deg) = infinite. Note that it does not depend on the weight. Only the frictional force depends on weight Ff=Fn*Mu. Here is the derivation:

(1) Definitions:
Mu = coeficient of static friction
W = weight of material (block, for example)
Theta = Angle above horizontal
Fn = Force Normal to the incline
Ff = Frictional force parallel to the incline

(2) Ff = Fn*Mu (definition for Mu)
(3) From geometry sin(Theta)=Ff/W & cos(Theta)=Fn/W
(4) Substitute (2) for Ff and Sin(Theta)=Fn*Mu/W
(5) tan(Theta) is defined as sin(Theta)/cos(Theta) so:

Tan(Theta) = (Fn*Mu/W) / (Fn/W)

(6) Simplify and cancel terms ... Tan(Theta) = Mu

-Paul