A general question about static/kinetic friction

On an inclined plane, sometimes the force applied is up the incline,sometimes it's down the incline BUT sometimes it's stationary. My question is, when do you ADD the Rn value with mgsintheta and when do you subtract these? Thanks.

easy way to know that is to draw the free body diagrams

say the incline is A degs inclined

to find the force of friction you have to know the normal force that is calculated from the force of the surface pushing up on the block but the surface is tilted

you are given A is the angle usually

............................n
s.......................n
.........s...........b
....................rw
..................r...w.....s
................r......w........A.....…
........................w.............…


s is the ramp
n is the normal vector and direction
r is the portion of gravity pulling down on the block
magnitude of n = magnitude of r if no other forces applied with a component that is along the n vector

w vector is the wieght of gravity pulling straight down

with this diagram you can see that tilting the angle less decreases the angle between r and w

and increasing the tilt of the ramp increases the angle between r and w

this means and between r and w = A the tilt of the ramp

you can use a few triangle and angle laws but thats the result


this means that the amount of gravity pulling down the ramp is mgsin A
the A is the same as the theta I assume(depending on the diagram ) will use A here

because A is the angle between r and w

and we know w = mg
so

since sin A = Framp/mg

solving for Framp = mgsin A

this will ALWAYS be down the ramp if the object were to be moving down the ramp then friction would be pushing up the ramp so friction would be - or negative since we picked down as positive

Fnet = sum of the forces