What is the answer to this physics riddle?

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Discussion Overview

The discussion revolves around a physics riddle involving the comparison of two paths taken by balls under the influence of gravity, with considerations of height differences and potential frictionless conditions. Participants explore various hypotheses and mathematical approaches to determine which path results in a faster travel time.

Discussion Character

  • Debate/contested
  • Mathematical reasoning
  • Exploratory

Main Points Raised

  • Some participants suggest that if the start and stop height differences are the same, the answer might be C.
  • Others argue that if the lines are frictionless, the path taken should not matter.
  • A participant proposes a mathematical approach to calculate the average velocity of the balls based on their height profiles and angles.
  • Another participant questions whether all paths below a flat line are guaranteed to be faster, suggesting that specific path shapes need to be analyzed.
  • Some participants note that the initial velocity of the balls complicates the comparison, indicating that certain paths may be faster depending on this factor.
  • One participant emphasizes that the relationship between the paths and the time taken is not straightforward and requires detailed calculations.
  • Another participant mentions that a journey with variable heights may generally take longer than a flat journey, using an exaggerated example to illustrate this point.
  • Several participants express uncertainty about the implications of their calculations and the conditions under which one path may be faster than another.

Areas of Agreement / Disagreement

Participants do not reach a consensus on which path is definitively faster, with multiple competing views and ongoing debate about the influence of initial velocity, path shape, and height differences.

Contextual Notes

Limitations include the lack of specific data regarding the paths and the initial conditions, as well as unresolved mathematical steps in the proposed calculations.

  • #31
Borek said:
Then how come brachistochrone exists, if time on all curves is identical?
But it isn't one. The more on kinetic energy gained downwards is lost again upwards. (But I haven't done the math, maybe it doesn't cancel out, however I think it does. I desperately try to remember the analogous experiment in a math museum I once visited, I thought they were equally fast at the finish ...)
 
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  • #32
fresh_42 said:
But it isn't one. The more on kinetic energy gained downwards is lost again upwards. (But I haven't done the math, maybe it doesn't cancel out, however I think it does.)

The final speed must be the same (without friction) but the ball will take different times for different paths. For example, you can have a path with a time to the lowest point as large as you wish!
 

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