I Gravitational Illusions -- Two balls rolling down differently-shaped ramps

AI Thread Summary
The discussion centers on the concept of gravitational illusions, specifically how two balls roll down differently-shaped ramps. Participants emphasize the importance of hands-on problem-solving to truly understand the physics involved, rather than relying solely on mathematical proofs. The Brachistochrone curve is mentioned as a relevant mathematical solution to the problem of determining which ball reaches the bottom first. Contributors are encouraged to share their own mathematical solutions for feedback and discussion. Engaging with the problem directly is highlighted as essential for deeper learning.
Jurgen M
Without this test,using only math, would you prove that left ball will comes first?

 
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Why make us do all the work? You'll never learn unless you do the problems yourself.

Write your own mathematical solution and post it here. We'll comment on it.
 

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I am reading the Griffith, Electrodynamics book, 4th edition, Example 4.8 and stuck at some statements. It's little bit confused. > Example 4.8. Suppose the entire region below the plane ##z=0## in Fig. 4.28 is filled with uniform linear dielectric material of susceptibility ##\chi_e##. Calculate the force on a point charge ##q## situated a distance ##d## above the origin. Solution : The surface bound charge on the ##xy## plane is of opposite sign to ##q##, so the force will be...
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