Question #d6539

1 Answer
Jul 24, 2015

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#.

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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#).