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

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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.
 
Thread 'Why higher speeds need more power if backward force is the same?'
Power = Force v Speed Power of my horse = 104kgx9.81m/s^2 x 0.732m/s = 1HP =746W Force/tension in rope stay the same if horse run at 0.73m/s or at 15m/s, so why then horse need to be more powerfull to pull at higher speed even if backward force at him(rope tension) stay the same? I understand that if I increase weight, it is hrader for horse to pull at higher speed because now is backward force increased, but don't understand why is harder to pull at higher speed if weight(backward force)...

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