In which direction would friction act in a limiting equilibrium on an inclined plane?

If a force is applied to an object on an inclined plane in the upward direction of the plain in order to balance the component of weight such that the object is in equilibrium, in what direction would the friction then act?

• If your applied force completely cancels the component then the friction would not work in any direction. Because there is motion or tendency of motion. Jan 25, 2017 at 6:40
• Please add a sketch. This very much depends on directions as well as magnitudes, so your answer is not clear Jan 25, 2017 at 9:19
• @Steeven added a sketch. Jan 25, 2017 at 10:44
• @mockingbird But In Which direction would the component of friction work? In The direction of Weight or applied force?? Jan 25, 2017 at 10:45
• @Saha19 I am telling this again there won't be friction force if the initially static object is subjected to zero net force. But if there is net force, then friction will act on the opposite of friction force... Jan 25, 2017 at 13:09

You can't know. Friction can go in both directions depending on if $F$ is larger or smaller than the weight component.

• If $F$ is larger than the weight component, then friction must be down along the incline (in order to hold back, since gravity isn't strong enough).

• If $F$ is smaller, then friction must be upwards along the incline in order to help $F$ (otherwise $F$ couldn't hold it)

• If $F$ is exactly equal to, then there is no friction.

Remember that we are talking about static friction here. And static friction is a force that adjusts itself to whatever is necessary for keeping something still. Both direction and size is adjusted to fit, so it purely depends on the circumstances (on other forces).

• Sir, I had a question, what if the object is a round object and friction completely cancels out the weight of that object (assuming it is acting upward), that is, $mg \sin \theta=\mu mg \cos \theta$, so it's acceleration would be $0$ but still it would have a net torque, so will it still move downwards? Would it be a rolling motion or will it slip on the plane? I can't understand how it will move downwards when there is no force in the downward direction now..
– V.G
Jan 12, 2021 at 16:16
• OR friction simply acts in the downward direction adding to it's component of weight, but then, if that is the case, it would experience a clockwise torque and rolling cannot occur, so is it that it initially acts downwards, gives it a downward motion, then starts acting upward?
– V.G
Jan 12, 2021 at 16:25
• @Vilakshan Those are good questions but it wold be easier to answer to if you create it as a new question Jan 12, 2021 at 17:16
• My experience on this site is not good actually, whenever I ask questions here, they either get closed and marked as homework and exercises, that's the reason I asked here in person.
– V.G
Jan 12, 2021 at 17:18
• Still, I asked the question, you can see it here.
– V.G
Jan 12, 2021 at 17:40