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Pad 7:58 PM 75% a session.masteringphysics.com Women's Sweatshir... MyLab and Mastering Course Home MasteringPhysic... Course Home HW-9 Problem 9.52 « previous | 10 of 15 next Problem 9.52 A uniform marble rolls down a symmetric bowl, starting from rest at the top of the left side. The top of each side is a distance h above the bottom of the bowl. Part A How far up the right side will the marble go if the interior surface of the bowl is rough so that the marble rolls without slipping? Express your answer in terms ofh Submit My Answers Give Up Part B How high would the marble go if the bowl's surface were frictionless? Express your answer in terms of h Submit My Answers Give Up Part C For which case is the marble moving faster when it reaches the bottom of the bowl? O The case for the bowl with the rough surface O The case for the bowl with the frictionless surface. Submit My Answers Give Up Continue

Explanation / Answer

Let the marble be released from a vertical height h (height of the bowl).
During the downward motion, it is rolling purely. so
    v=rw
Let the mass be m.
Potential energy at h = K.E. at the bottom
So, mgh = 1/2 mv2 + 1/2Iw2

Here w is the angular speed at the bottom.
       mgh = 1/2mw2r2 + 1/2 X 2/5mr2w2
         gh = 7/10r2w2      
    i.e.,  r2w2 = 10gh/7   .............................(i)
Since no external torque acts on the upward journeyso w remains same.
At maximum height H
v = 0.
So, K.E. possessed by the body =1/2.2/5mr2w2
So, K.E. lost = 7/10 mr2w2 - 1/5mr2w2 = 1/2mr2w2

This lost energy is gained in d form of P.E.
So,
   mgH= 1/2 mr2w2
So, H= 1/2 . 10/7gh    (from (i))
      H = 5/7 h

Part (b)

lossin K.E. = 7/10 mr2w2

This is gained as P.E.
So,     mgH = 7/10mr2w2
                  H= (7/10) *(10h/7)
       So,   H=h

Part (c).

with friction , the marble has rotational kinetic energy as well as translational kinetic energy which ensures greater height for marble.

Hence first option is correct.

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