Dr. L. is super tired of rocking Kepler to sleep so he devises the Kepler Ball S

Question

Dr. L. is super tired of rocking Kepler to sleep so he devises the Kepler Ball Sleep SystemTM for her. It consists of putting Kepler in a sphere of Radius R (total mass M) and dropping her into a U shaped track. The Kepler Ball TM makes smooth transitions between all sections of the track. The Green section is to be considered perfectly level with ground and the tops of the red and blue sections are vertical relative to ground. When it rolls on a friction-able surface, The Kepler Ball TM does so without slipping.

He starts by letting her go at a height H above the flat bottom of the track such that the center of mass of the Kepler Ball is 5R above the green section. You can approximate the Kepler BallTM as a solid sphere.

1.) If the entire track is frictionless is the Kepler BallTM rolling as she passes through the green section ( YES / NO )?

2.) If only the blue section of track has friction, will the Kepler BallTM be rolling as it goes across the green section ( YES / NO )?

3.) If only the blue section of the track has friction, how high up the red side does she go? Your answer should only be in terms of R!

4.) Also, is the Kepler BallTM rolling at the maximum height ( YES / NO )?

Explanation / Answer

1.) If the entire track is frictionless is the Kepler BallTM rolling as she passes through the green section ( YES / NO )?

2.) If only the blue section of track has friction, will the Kepler BallTM be rolling as it goes across the green section (Yes )

3.) Hmax = 5R ( 1/1.4)

Hmax = 3.571 R

4.) Also, is the Kepler BallTM rolling at the maximum height ( YES )?

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