posted by Melissa .
how does the slope of a Ff-Fg graph relate to the coefficients of friction , prove it mathematically.
I am not sure that I understand what you mean.
If Ff is the friction force and Fg is the weight (on a level surface), then
Ff = Uk* Fg if the object is moving.
Ff = Us* Fg is the maximum static friction force that keeps it from moving.
Us and Uk are the static and kinetic friction coefficients, respectively. They become the slopes of the Ff vs Fg fucntion.
On a slope of á degrees, Fg is replaced by the "normal component" Fg cos á