Task with ball, cyllinder and inclined plane - problem -help

[Pawell]

Hello everybody! ;)

I've got problem with task below, I've got few days to solve it and I've got some troubles:

On inclined plane with variable angle of inclination we set cylinder and ball on the same height above the ground. The friction factor for both objects comes to 0,1 - it's the same and constant for both of them. Compare the times, after which both of these objects reach the base of inclined plane (the ground) - count the ratio of these times. Consider two situations:

a) for small angles of plane's inclination, when movement of bodies is held without slip.
b) for big angles of plane's inclination, when movement of bodies is held with slip.

Calculate, for what range of angles situations a) and b) are considered.


I've no problem with situation in point a). But I can't manage the situation b) because I think these "times" depend on angel too - not only on friction factor and inertial moment of bodies. How to solve this? Have no idea.. I've thought about this very long time and still nothin' ;) If you know, please help me. I'll be very grateful even for little help :)

 

[LowlyPion]

Welcome to PF.

If I am understanding your question right, maybe look at the relationship between the normal force that defines the force with which tangential acceleration will be imparted to rotational kinetic energy. As the angle steepens won't the force normal to the incline lessen and hence its ability to rotationally accelerate the objects will diminish at the same time as the force parallel to the plane increases, accelerating the object faster than the surface can spin the objects to keep up?

In the extreme case of 90° it will skip rather dramatically one would think.