What determines the direction of static friction forces?

• rhotonsix
In summary: - the plane is at a consistent height and angle- the rope has a uniform density- the rope is fastened at the top
rhotonsix
My understanding of static friction is that it is a resistive force in response to an applied force. I recently read the following example. A rope of uniform density, length L, is fastened to a plane with incline angle “theta” along its length. The question asks for the tension at the top of the rope where it is fastened to the plane. The solution states that the direction of the static friction depends on how the rope arrived on the plane - if it is simply placed on the plane and fastened the static friction points up the plane, while if the rope was dragged up the plane and fastened, the static friction force points down the plane. This in turn will affect the tension. I get why if one drags the rope up the plane there is a resistive kinetic friction force in the opposite direction. But it seems to me that once the rope is fastened on the plane and is at rest, the forces it experiences are the same regardless of how it got there and hence the static friction would be the same. Where am I wrong? Thanks in advance.

rhotonsix said:
Summary:: Why does the direction of static friction on an object depend on how the object was placed on the surface?

My understanding of static friction is that it is a resistive force in response to an applied force. I recently read the following example. A rope of uniform density, length L, is fastened to a plane with incline angle “theta” along its length. The question asks for the tension at the top of the rope where it is fastened to the plane. The solution states that the direction of the static friction depends on how the rope arrived on the plane - if it is simply placed on the plane and fastened the static friction points up the plane, while if the rope was dragged up the plane and fastened, the static friction force points down the plane. This in turn will affect the tension. I get why if one drags the rope up the plane there is a resistive kinetic friction force in the opposite direction. But it seems to me that once the rope is fastened on the plane and is at rest, the forces it experiences are the same regardless of how it got there and hence the static friction would be the same. Where am I wrong? Thanks in advance.
It can depend on whether the rope is itself under tension. The static friction makes up the difference between the other forces on each segment of the rope.

A clearer example would be a block attached to a spring. If the spring is at its natural length, then the block is trying to slide down the incline. If, however, the spring is extended it will be trying to pull the block up the incline. Static friction on the block will be in opposite directions in those two cases.

Lnewqban
rhotonsix said:
Summary:: Why does the direction of static friction on an object depend on how the object was placed on the surface?

My understanding of static friction is that it is a resistive force in response to an applied force.
Both the magnitude and the direction of static friction are whatever is needed to prevent slipping.

vanhees71 and etotheipi
rhotonsix said:
But it seems to me that once the rope is fastened on the plane and is at rest, the forces it experiences are the same regardless of how it got there and hence the static friction would be the same. Where am I wrong?
You're neglecting the fact that the rope will stretch as you drag it up the slope. When you stop dragging, it's not guaranteed that all parts of the rope will continue to move far enough to get the rope back to its unstretched length.

Lnewqban and Dale
rhotonsix said:
But it seems to me that once the rope is fastened on the plane and is at rest, the forces it experiences are the same regardless of how it got there and hence the static friction would be the same.
But which forces would that be? There are many combinations of friction and fixation force that would keep the rope in equilibrium.

https://en.wikipedia.org/wiki/Statically_indeterminate

rhotonsix said:
... But it seems to me that once the rope is fastened on the plane and is at rest, the forces it experiences are the same regardless of how it got there and hence the static friction would be the same. Where am I wrong? Thanks in advance.
I would replace the idea of anchoring the rope with clamping the top end of the rope against the plane, only to avoid manipulation of the rope along the surface of that plane.

If we drop the rope on the plane, it will naturaly tend to slide down the plane.
If it doesn't, we have enough static friction force and we don't need the clamp: friction force vector is pointing up the plane.

If it does slide down, we have dynamic friction opposing that movement; then, we clamp the top end of the rope and stop the sliding movement, which increases the value of the friction force from kinetic to static, but without changing the up-slope direction of its vector.

Imagine that the plane-oriented component of any external force is appied to the center-line of the rope, while friction force is applied onto the bottom surface line.
There is a minor but real elastic deformation of the fibers of the rope.
Because of that, in this case, any paired point of the top surface line will be a little displaced down the slope respect to its pair at the bottom surface line.

Thank you for all the insightful comments. Lnewqban, I initially approached the problem with the thought process you describe but when the solution included the scenario where the rope is dragged up the plane and fastened is where I got confused. As Vela said, I neglected the stretch associated with dragging the rope up the plane, which I think is determined by both internal factors and external forces (g and friction, which is initially static, then kinetic as it is being dragged, and then static again once at rest) and the residual stretch is the tension force experienced by the top of the rope where it is fastened to the plane. At least this makes sense to me based on my novice conceptualization lol.

Dale and Lnewqban

1. What is static friction and how is it different from kinetic friction?

Static friction is the force that prevents two surfaces from sliding past each other when they are in contact and at rest. It is different from kinetic friction, which is the force that opposes the motion of two surfaces that are already in motion.

2. What factors determine the direction of static friction forces?

The direction of static friction forces is determined by the normal force between the two surfaces, the coefficient of static friction, and the angle of the surfaces' contact.

3. How does the coefficient of static friction affect the direction of static friction forces?

The coefficient of static friction is a measure of the roughness or smoothness of the surfaces in contact. A higher coefficient of static friction means that the surfaces have a stronger grip on each other, resulting in a larger static friction force in the opposite direction of motion.

4. Can the direction of static friction forces change?

Yes, the direction of static friction forces can change if the factors that determine it change. For example, if the angle of the surfaces' contact changes, the direction of the static friction force will also change.

5. How does the direction of static friction forces affect the motion of objects?

The direction of static friction forces plays a crucial role in determining whether an object will remain at rest or start moving. If the static friction force is greater than the force applied to the object, it will not move. However, if the applied force is greater, the object will start moving in the direction of the applied force.

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