Let's assume we have a 1 kg cube on a flat uniform surface. The coefficients of friction between them are $\mu_k = 0.25$ and $\mu_s = 0.50$. This cube is moving at 1 m/s in the y direction, with whatever force is needed to overcome friction being applied. There is no force or motion in the x direction. Assume $g = 10\, {\rm m / \rm s^2}$ in the z direction.
Now, if a force is applied in the x direction which type of friction applies, static or kinetic? Edit: To clarify, if the cube is moving forward, and gravity is acting down, the new force is being applied to the right.
My rudimentary model of friction is that it acts like two pieces of sandpaper where the bumps can interlock when there is not motion, but when they are moving over top of each other they don't have time to settle in. In that model, I would think kinetic friction would apply, as the direction of movement shouldn't matter.
However, I realize that in reality friction is a result of molecular attractive forces, and probably a lot of other more complicated things I'm unaware of. Because of this, I suspect the answer may lie somewhere between static and kinetic friction.
Best Answer
I can´t fully come up with an explanation from more basic principles, but in the case you describe you will have kinetic friction. Or at least that is what all engineering books say...
There are a number of situations where this effect is clearly demonstrated:
While not entirely the same, a similar situation arises when a car rolling down a road with a strong side wind brakes and locks the wheels. While the wheels were rolling, there is no relative motion between the road and the tire, so there is static friction in effect, and unless the wind is really strong, as in a hurricane, the force will not overcome friction and the car will not skid sideways. Once the brakes are locked, the car starts skidding forward, because the force due to the inertia of the car overcomes friction. Once this happens, the car will also start skidding sideways, due to two factors:
the lesser important is that the coefficient of friction in effect once there is relative motion is the kinetic, not the static one.
the main effect is due to the fact that the direction of movement doesn't really matter at all: at the contact point you have a force due to inertia and a force due to the side wind, and once their combined magnitude exceeds friction, you will start having movement in the direction of that combined force, so forward but also to the side.