Does Increasing the Elevation Affect Maximum Static Friction?

[ap_cycles]

Hi,

I place an object on a rough surface.

It is clear that the static friction will increase as you increase the elevation of the surface since there is a bigger component of weight acting down the plane surface.

But will the max static friction -i.e. friction at the verge of slipping be the same, even when you increase the elevation? I can't put a pulse to it, but my strong hunch is no.

What do fellow forummers think?

 

[graphene]

Elevation? How does elevation come into picture?

 

[rcgldr]

I assume he means elevate one end of the surface so its angled. Ideally, maximum static friction should be independent of angle, but in the real world there may be slight difference depending on the overall direction and magnitude of force and the size of the contact area.

 

[Lohrasp]

So I am going to make some assumptions here:

1. by the increase in static friction, you mean the static friction force.
2. if you incline the plane, the static friction force DOES NOT increase because more force is exerted in the direction perpendicular to the plane. It increases because more force is exerted in the direction parallel to the surface. This is due to friction obeying Newtons third law. So basically friction will scale itself with the force that wants to move the object.

Ok now that we have these things out of the way, here's some equations that might help you in understanding this

F_Friction = \mu_{static}mgcos(\theta)

where \theta changes between 0 and pi/2. \mu_static is the static friction coefficient of the material.

and the force parallel to the surface which wants the object to slip is

F_Parallel = mgsin(\theta)

so if you put these 2 equations with the domain D [0,pi/2] the point that they intersect will be the "Slipping point" and it will always be the same, and would ONLY depend on \mu_{static} which in terms would ONLY depend on your material and surface of contact.
Although if you mean if the static friction force at the slipping point is different or not for each different elevation, the answer is yes, it is. As you increase the elevation its the same as a lower mass on a horizontal plane in which case the maximum static friction force would be less.

I hope this helped, but your question was a bit vague. If my explanations did not help, feel free to clarify the question for me and i will try to help you more.

 

[ap_cycles]

Dear fellow forummers and Lohrasp in particular,

Thanks for the replies. Yes, Lohrasp, you have interpreted my question correctly, and YES, i understood your explanation.

Thanks!