### A uniform marble rolls down a symmetric bowl

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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. The left half of the bowl is rough enough to cause the marble to roll without slipping, but the right half has no friction because it is coated with oil. Part A How far up the smooth side will the marble go, measured vertically from the bottom? Express your answer in terms of h. h' = _______________________ Part B How high would the marble go if both sides were as rough as the left side? Express your answer in terms of h. h'' =__________________________

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