How does one know the direction of static frictional force?

Question

I've provided an example in the form of a photo. This is a question taken from an exam paper. In this example, there are 2 forces acting on the object aside from friction, the applied force and tension. The applied force and tension are balancing each other out and the object is stationary so my question, is how do I know what the direction of static friction is? In an example where there is only one applied force acting on the object and if the object remains stationary, then it is is easy to see that the static frictional force will be equal in magnitude but opposite in direction to the applied force. That is mostly to do with objects on an incline, but for this example with no incline, how do I know the direction of static friction? Thank you in advance to anyone who answers.

Old Science Guy · Answer

...
in this problem
if the rope balances the hanging weight
Fcos30 = 7.5 (9.8) = 73.5 N
F = 84.9 N or 85 N
but F could be as great as
Fcos30 = 73.5 n + 0.45 (9.8) (12) = 73.5 + 52.92 = 126.42
F = 146 N
or as little as
Fcos30 + 52.92 = 73.5
F = 23.8 N or 24 N
so F falls in a range while there is still equilibrium
146 N > F > 24 N

frictional forces are a reaction to the tendency toward motion
and are opposite to that direction
so
in the first example above friction is 0 and has no direction
in the second example friction is 52.92 N and is directed to the right
in the third example friction is 52.92 N and is directed toward the left
so friction varies from 0 N to 52.92 N
and its direction is right if F is greater than 85 N
and direction is left if F is less than 85 N

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Morningfox · Answer

If the table was frictionless, would the block move?  If it would not move, then the static friction is zero.  If it would move, then the static force is just enough, and in the right direction, to keep it from moving.

For your example, you could assume that the static friction force acts to the right, and solve for F.  When you get a negative value for the friction force, then it actually acts to the left.

==========
I get F = 11.82 Kg(force) = 115.87 N (depends on force of gravity).
The block is almost moving to the left .. a bit larger F would move it to the left.
The friction force is acting to the right.

? · Answer

The force of friction (static or otherwise) ALWAYS ACTS to prevent motion or to impede motion.  The ONLY direction that motion might take place in the pictured example is defined to be to the RIGHT because F is said to be preventing motion.  Static friction must also prevent motion (ref: 1st sentence) so it too must act in the SAME general direction as F (actually the DIRECTION is the F x-axis component direction).  The "line of action" of all friction forces will be PARALLEL to the impending motion direction, or in the case of moving objects, the actual motion direction

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How does one know the direction of static frictional force?

3 Answers