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

Question

Dr. L is super tired of rocking Kepler to sleep so he devises the Kepler Ball Sleep System^TM 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 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 Ball^TM as a solid sphere. 2a) If the entire track is frictionless is the Kepler Ball rolling as she passes through the green section YES NO be rolling as it goes across the green section (YES/NO)? 2b.) 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! Also, is the Kepler Ball rolling at the maximum height (YES NO

Explanation / Answer

1. Yes, because in case of frictionless the gravitational frictionless is zero but the frictionless applied by the mass of the ball doesn't zero. Due to this the body slides to the green section.

2. Due to presence of slide here or an angle, the body rolls down to the green section after passing through blue section.

3. by the conservation of total mechanical energy of the body, its energy at any other point on the section is:

TE = PE + KE

TE = mgh + 1/2 mv2

P E = T E

gH = gh + 1/2 v2

5R = h + 1/2 h

H = 10/3R

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