[Physics] Negative friction force, positive normal force

Question

I realize that formulas don't always tell the whole story, but there seems to be some information missing from the equation: $F_f=\mu F_N$

Imagine we say up and right is positive. Then if an object is moving across a surface to the right, the friction force should be negative (acting against the positive applied force), and the normal force should be positive (acting against the gravitational force).

Let's say: $F_N=882\ \text{N}$ and $\mu=0.600$, then: $F_f=0.600\times822=529\ \text{N}$, which is positive, when it should be negative.

I realize that this formula converts between axes, so there can't be a reliable way to relate the signs, but then what is the convention? Does this formula just provide an absolute value for friction, and you can set it positive or negative, depending on the situation?

Answer 1

It would probably be wiser to state the friction law as:

$$|F_F|=\mu |F_N|$$

where $|F_N|$ denotes the modulus of the Normal force.

Now consider the following diagram:

Both blocks and slopes are identical.

1. Left: some net force on the block causes an acceleration $a$ (left and up). The friction force $F_F$ points in the opposite direction: it opposes relative motion.
2. Right: some net force on the block causes an acceleration $a$ (right and down). The friction force $F_F$ points in the opposite direction: it opposes relative motion.

So the friction force opposes relative motion between the sliding surfaces.