Which would be faster: A ball rolling down a ramp with no groove

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AI Thread Summary
A ball rolling down a ramp with no groove is generally expected to be faster than a ball rolling down a ramp with a groove due to the reduced friction and potential energy loss in the groove. The radius of the ball does not significantly affect the speed in this scenario, as the groove primarily alters the path rather than the rolling dynamics. Analytical proof can be derived from principles of rotational motion and energy conservation, showing that the groove's impact is minimal. The discussion emphasizes the importance of understanding the mechanics of rolling motion without external resistance. Overall, the consensus suggests that the groove does not enhance the speed of the ball.
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Homework Statement


Which would be faster: A ball rolling down a ramp with no groove, or a ball rolling down a ramp with a groove?
What effect does the radius have, if any? Disregarding resistance and whether or not the ball rolls in a straight line.

Homework Equations





The Attempt at a Solution




I thought that a decrease in rolling radius due to being in the groove might have an effect but apparently not. Any input appreciated.
 
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