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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. (a) How far up the right side of the bowl will the marble go if the interior surface of the bowl is rough so that the marble rolls without slipping? (b) How high would the marble go if the bowl’s surface were frictionless? (c) For which case is the marble moving faster when it reaches the bottom of the bowl?
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