Friction between a mass and a conveyor belt (ENGAA 2017)

[TomK]

Homework Statement

ENGAA 2017 - Question 50

Relevant Equations

F ≤ μR

Please scroll-down to Q50: https://www.undergraduate.study.cam.ac.uk/files/publications/engineering_s1_qp_2017.pdf

The correct answer is 'B', or 'mgsin(Θ)'. I put 'E', or 'μmgcos(Θ)'.

There are unofficial worked solutions which I have been referring to when I have attempted the question and don't understand the correct answer: http://www.engineeringadmissionsassessment.com/2017-solutions.html

This is what the worked solution states:
"Recall that frictional forces increase to match any opposing forces up to a maximum (which has not been achieved in this scenario).
The suitcase is not in limiting equilibrium so the frictional force up the plane must equal the force due to gravity resolved down the plane so the force is mgsinθ."

I am having trouble understanding when an object is in limiting equilibrium. How do you know when friction is at its maximum, when the object is on a moving, rough surface like a conveyor belt? Is it just because the question states "the suitcase does not slip"? Would I be right in saying that there is maximum friction when an object slips?

 

[haruspex]

When the surfaces slide over each other it is kinetic friction, which is generally a bit less than maximum static friction.
If the surfaces are not sliding, you can only assume the frictional force is at maximum if you are told something to indicate it, like "about to slip".
In the question you attach, there is enough information to answer B without having to consider if it is at max. They even tell you, redundantly, that it is not.

 

[gneill]

Moderator's note: For homework questions is is preferable to include the text of a problem statement directly rather than post a link to a off-site sored file that could disappear at any time. If the file disappears for some reason, the thread becomes useless. It is also a courtesy to others to not require them to download a large PDF file in order to see the question.

So, for example, here's a "snip" of the question from the PDF:

 

[TomK]

When the surfaces slide over each other it is kinetic friction, which is generally a bit less than maximum static friction.
If the surfaces are not sliding, you can only assume the frictional force is at maximum if you are told something to indicate it, like "about to slip".
In the question you attach, there is enough information to answer B without having to consider if it is at max. They even tell you, redundantly, that it is not.

Did I answer my own question in the final paragraph of my post? If so, I think that's all I needed to know for this problem. I believe it makes sense to me now.

 

[haruspex]

Homework Statement:: ENGAA 2017 - Question 50
Relevant Equations:: F ≤ μR

Would I be right in saying that there is maximum friction when an object slips?

Not quite. As I wrote, once it is slipping the friction is kinetic, which tends to be a bit less than the max static friction. The maximum frictional force is just before it slips.