Conservation of energy of a marble problem

AI Thread Summary
The problem involves a marble rolling down a symmetric bowl, starting from rest on a rough left side and moving to a frictionless right side. The key concept is the conservation of energy, which states that the total mechanical energy remains constant in the absence of non-conservative forces. The discussion clarifies that since the marble rolls without slipping on the rough side, no energy is lost to friction, as there is no heat generated at the contact point. The question posed is about the relevance of friction in calculating the marble's motion, emphasizing that it does not affect the conservation of energy in this scenario. Understanding these principles is crucial for determining how high the marble will ascend on the smooth side.
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Homework Statement


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. (a) How far up the smooth side will the marble go, measured vertically from the bottom?


Homework Equations



Conservation of energy

The Attempt at a Solution


While applying conservation of energy, why we should not consider the work done by the friction force on the marble? Kindly explain me.
 
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Because the marble rolls without slipping, there is no heat generated at the point of contact so no Joules are lost to friction. For heat to be generated, the two surfaces need to rub against each other.
 
ok, Thanks :)
 
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