Question

Question #d6539

Answer 1

When you say frictional force, I am assuming you just mean friction. I will also suppose we are using an example where we have a smooth wooden block sliding down a semi-rough inclined ramp. Thus I will be referring to static friction, which I will call `F_s`.

Friction is in some sense a reaction force (although strictly speaking it is not, it is intuitive to call it that for a reason I will get to in a moment), because it decreases as the incline angle increases since the parallel component of the force due to gravity starts to vanish; at an angle perpendicular to the flat surface on which the ramp is laid, there is only the vertical component to the force due to gravity (`F_g`).

The parallel component of the force due to gravity might be called `F_(g||)`. When you draw the Free Body Diagram of this situation, you have `F_(g||)` pointing along the ramp downwards, `F_(g_|_)` pointing inwards and perpendicular to the ramp surface, `F_N` (the Normal Force) pointing opposite `F_(g_|_)`, and the static friction force (in this case), `F_s`, pointing along the ramp upwards. Since the direction of `F_s` is opposite that of `F_(g||)`, as `F_(g||)` vanishes, so does `F_s`.

You can tell that this occurs since the wooden block starts to slide down the ramp as the angle increases, indicating a lower coefficient of static friction (and thus a lower static friction) along the ramp and proving that its magnitude is proportional to the magnitude of its opposing force. That is why I said it was intuitive to call it a "reaction force", even though it is not reacting to an applied force.

A fun problem with friction is:

At what angle would a wooden block on a ramp not slide down, if `mu_s` is `0.2`?

`F_(g||) = mgsintheta = -F_s`
`F_(g_|_) = mgcostheta = -F_N`
`F_N = -mgcostheta`
`F_s = mu_sF_N = -mu_smgcostheta = -mgsintheta`

`mu_s = tantheta`
`arctan(mu_s) = theta` for which the block is in static equilibrium.

`~~ 11.31^o`

with positive `x` being down the ramp and away from the ramp in the perpendicular direction (`y`).