The angle at which a skier will leave the sphere

[Orodruin]

Or, "some friction" can be interpreted as "non-uniform" (and also "not enough at any given point to stop the skier").

You can, but that still requires making additional constraining assumptions on the problem that are not part of the problem statement.

 

[kuruman]

You can, but that still requires making additional constraining assumptions on the problem that are not part of the problem statement.

It does indeed. There are additional unmentioned assumptions, such as "Assume that the skis and the skier is a point mass; however, although a point mass has no air resistance, assume that the force it is distributed over a finite area so that the skier does not sink in $~dots~$" and the list goes on. I am not being facetious. I am asking where, in an introductory physics problem statement, one draws the inclusion line of assumptions that are absolutely to necessary to answer the question. Too many listed assumptions detract, especially beginners who are not experienced enough to decide for themselves what is important. Students are unlikely to become engaged with introductory physics problems that read like legal documents

I draw a line at the point where the statement of the problem is not sufficient to result in an answer unless physically unreasonable assumptions are made. However, what's physically unreasonable, in my opinion, needs to be tempered by the pedagogical utility of the question. This particular problem requires the combination of mechanical energy conservation with dynamics and circular motion. Its utility is that it shows to students that the concepts they have seen in separate textbook chapters are integral parts of the same underlying reality. That, in my mind, is sufficient reason to overlook the fuzziness of the assumptions and the lack of specific initial conditions. I am OK with the idea of a point skier merrily sliding on a frictionless sphere on point skis having started from rest by being a bit to the side of the top or by being gently pushed. That takes care of part (a). In part (b) I am still OK with the idea that this skier started a bit off to the side at an angle that was already larger than the angle of repose.

I don't see any reason for drawing a line between parts (a) and (b). I think that the utility of part (b) is to reinforce the connection between energy conservation and dynamics made in part (a). Others may disagree with me and draw the line elsewhere. I am hoping that we can agree to disagree.

 

[Orodruin]

I don't see any reason for drawing a line between parts (a) and (b). I think that the utility of part (b) is to reinforce the connection between energy conservation and dynamics made in part (a). Others may disagree with me and draw the line elsewhere. I am hoping that we can agree to disagree.

We can of course agree to disagree. To me, the introduction of friction destroys the entire (idealised) model and the argument behind the solution.