Time taken to slide down a circle (friction)

[eddiezhang]

Homework Statement

A point mass (m) is acted on by gravity, the normal force, and friction (μN). It starts at the point A(0,1). It then slides down a circular 'ramp', stopping when it touches the x-axis at B(1,0). It does not leave the surface of the ramp.

Find the general time of descent.

Relevant Equations

Centripetal force, friction etc.

This is for a math report that I'm supposed to write, which means I'm not supposed to use conservation of energy. This makes life much harder... so please bear with me. I am interested to see how you'd solve this purely kinematically though (if it can be solved that way).

Please tell me if this is posted to the wrong place. I asked a similar question in a math forum to no luck (they told me to post on a physics forum, so here I am).

Attached is a pdf with some diagrams and my working.

Thanks so much for your help,
Ed

 

[PeroK]

My first thought is that I'd be surprised if this has a closed form solution. Especially with friction involved.

Conservation of energy would give you the final speed, but not the time.