# Can kinetic friction and static friction be independent of each other in rigid body motion?

Suppose that there is a block with mass $$m$$ on the horizontal plane, and there are two horizontal forces, $$F_x=(a,0)$$ and $$F_y=(0,t)$$ acting on the block, where $$a$$ is constant.

Suppose further that at time $$t=0$$, the block is already moving in the direction of the $$x$$-axis, due to $$F_x$$. If the force $$F_y$$ varied depending on time as given above, how would $$F_y$$ be opposed by friction over time?

My first assumption was that, since the block is not moving at all in the direction of $$F_y$$, static friction would oppose $$F_y$$ until it reaches the threshold value $$F_y = \mu_s mg$$, independent of any movement in the $$x$$-direction. And after that as the block slowly gains velocity in the $$y$$-direction as well, while this time the friction does not act independently, but jointly, against the net force of $$F_x$$ and $$F_y$$, namely $$(a,t)$$.

But experimenting with a simple block and surface proved otherwise, as even the smallest force in the $$y$$-direction while the block is moving in the $$x$$-direction, slowly pushed it in the $$y$$-direction as well.

So is it that friction only cares about the net force from the beginning, and as long as it is moving in any direction the frictional force is kinetic?

(Apologies in advance for any grammatical mistakes I might have made, I am not a native English speaker.)

• I think if you imagine it as a circular movement, you will see intuitively that directon doesn't matter as long as it is moving. Apr 18, 2021 at 2:49

Once the force $$F$$ upon the body exceeds the static frictional force $$F_{static} = \mu_{static}.R$$, the body will be accelerated, thereafter, the kinetic friction will act upon it. The static friction coefficient is irrelevant now.