I had a question which has always been of slight confusion to me. Say you are dealing with your typical block-on-an-angled-plane setup.
You have a block with mass m that is initially at rest. The block sits on a surface at angle θ to the ground, has coefficient of kinetic friction μk, and a coefficient of static friction μs. There is an external force F acting on the block parallel to the ground. I am wondering, if you are given this setup, how to determine the direction of friction without first determining the direction of motion?
In this case the external force opposes the force of gravity.
To avoid the static case, let's set μs = 0, so the block would move immediately.
Now say we take the relevant components, F|| and Fg,||, as the two forces as forces which will determine the direction of motion of the block. We now have two scenarios, if the residual force
Fnet = F|| - Fg,||
Say we defined up the plane as positive. We will now consider the two possibilities:
If Fnet > 0, the applied force is greater and the block moves up the plane with Fk < 0, opposing motion and directed down the plane.
If Fnet < 0, the gravitational force is greater and the block moves down the plane with Fk > 0, opposing motion and directed up the plane.
My question comes in at this point, if this analysis is not performed how is the direction of motion determined?
F = ma = Fk - Fg,|| + F|| = Fk + Fnet
ma = (+/-)Fk + Fnet
An attempt to clarify my question:
My question was directed only at the direction of kinetic friction, for simplicity's sake imagine that the coefficient of static friction is 0 (μs = 0) or that the force interaction is so great that it is relatively 0 (Fnet >> Fs). Or that we are concerned only with the block after it has overcome Fs, and then the question can be analogized to the static case, and finding which direction the block moves.
Under these conditions it can be imagined that the block will move immediately.
It can be simplified to "how to determine direction of motion" if it suits you better, as I am aware that Kinetic friction is a reactionary force, so my question does indeed boil down to this.
Given the setup provided: Block on an inclined plane, External force opposing gravity, no static friction, and block initially at rest. Which of the following three options is the most trivial:
Solving for Fnet and inferring the direction of motion from the acceleration, which will then reveal the direction that kinetic friction will act
Other solution that does not involve first solving for Fnet first, essentially my question asks if this option exists, determining direction of motion without going into any grainy details of force interaction. If it does, then I would love it if someone could explain it to me, if it doesn't so be it.
Is there a way to determine the resultant direction of motion using a physical argument and not a mathematical one?