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I was watching Lecture 12 in Walter Lewin's 8.01 series (https://www.youtube.com/watch?v=djCCno4Cbcw), and the phenomenon at 19:26, as the ball bearing breaks through the surface, struck me. I have tried searching for any relevant math but it has been arbitrary. Are there any formulae that discuss the time taken or the forces acting in this case?

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