During a roller-coaster ride, a multi-car train is moving at a speed v towards a vertical loop of radius R. The length of the train is 8R. What minimum value of v would allow the train to pass the loop without any car ever losing contact with the track? Assume that the size of each car is much less than R. Friction is negligible.

Our September Challenge, “Let’s start with the ABCs,” drew many solutions from all over the world including many first-time contributors. We are pleased to recognize the following successful solvers:

  • Juan M. Aguirregabiria (University of the Basque Country, Bilbao, Spain)

  • Philip Blanco (Grossmont College, El Cajon, CA)

  • Phil Cahill (The SI Organization, Inc., Rosemont, PA)

  • David A. Cornell (emeritus, Principia College, Elsah, IL)

  • Sebastian de la Cruz (Pontificia Universidad Catolica del Peru)

  • Norman Derby (Southwestern Oregon Community College, Brookings, OR)

  • Don...

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