# Static friction force increases or decreases with increase in inclination until impending of motion?

Consider a block of weight W lying on the horizontal board.
As in the case when $\theta=0$ and we apply force parallel to board, friction force will increase until the impending of motion and equals to μN.
Does friction force fs increases also when inclined at some angle?
I think fs, the static friction force decrease because when the board is inclined Normal force becomes N=W $\cos\theta$, normal force decreases with increase in $\theta$.
Am I thinking right? If not then explain.
Or If I am right then it should be written in books that friction force decreases with inclination.

Remember that the maximum static frictional force is $\mu\, N$.

If the board is horizontal no frictional force is necessary to keep the block stationary.

Inclining the board will require there to be a static frictional force acting on the block equal in magnitude but opposite in direction to the component of the weight down the slope $mg\sin \theta$.

As $\theta$ increase so the static frictional force increases.

This continues until the angle of the board is such that the maximum static frictional force $\mu mg\cos \theta$ is equal to the component of the weight of the block down the slope $mg\sin \theta$.

So $\mu = \tan \theta$ and this the basis of a method for finding the coefficient of static friction.

You are correct in saying that the maximum possible static frictional force $\mu mg \cos \theta$ decreases with increasing board angle.

• I meant increase so it should read "The actual static friction force increases but it it less than the maximum static force which decreases as the angle increases.". – Farcher Apr 1 '17 at 18:15