How the coefficient of static friction works

[mvantuyl]

Not exactly a homework problem, but I'm trying to make sure I understand how the coefficient of static friction works.

Given an object on an inclined plane and a question which asks for the minimum angle at which the object will begin to slide, I know that the formula to use is:

mg sin([tex]\theta[/tex]) = [tex]\mu[/tex][tex]_{s}[/tex] mg cos([tex]\theta[/tex])

which becomes

tan[tex]^{-1}[/tex]([tex]\mu[/tex][tex]_{s}[/tex]) = [tex]\theta[/tex]

I understand that mg times the sin of the angle represents the force which is working against friction. Is mu mg times the cos of the angle equal to the normal force?

 

[tiny-tim]

Hi mvantuyl!

(have a mu: µ and a theta: θ )

I understand that mg times the sin of the angle represents the force which is working against friction. Is mu mg times the cos of the angle equal to the normal force?

No, mgcosθ is the normal force.

So µ_smgcosθ is the friction force, and mgsinθ is the component of the gravitational force which (in your terminology) is working against friction (and that's why they're equal).

 

[mvantuyl]

Thank you! That clears it up for me.