Can a coefficient value change? help

[northern expo]

this is a similar question to an earlier queestion but an interesting relationship occurred.

when finding an experiemental coefficient of friction between a brick and a wooden ramp we can determine this coefficient by applying a measureable force at a constant velocity and the weight of the object ( u = fa / fg ) where the fa is theforce parallel and fg is the force normal. no problem with this but as the ramp is elevated (creating an incline) and we look at the force parallel required to pull it up the ramp at a constant velocity and the force normal (cos angle x fg ) this relationship appears to an increasing value due to the increasing fa and a decreasing fn. is there something I'm missing or can i not find a coefficient value by pulling up an incline and only when allowing it to slide down the ramp?

I'm sure there is something simple I'm missing. any help?
also is there a standard value between wood and concrete?

 

[Woland]

There is more to the story than fa/fg when the ramp is inclined.

Ff = u Fn
u = Ff/Fn

Fn is mg cos(angle)
Ff is not equal to Fa like it was for the horizontal surface. Now Fa is being opposed by a part of Fg and Ff.

So we do a summation of forces along the path of motion (up the ramp) and set it equal to zero:
Fa - Ff - Fg sin(angle) = 0
Ff = Fa - mg sin(angle)

u = Ff/Fn = [Fa - mg sin(angle)]/[mg cos(angle)]

It should give you the same answer no matter what the angle is.