rock climbing and differential equations the fall factor n.
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Rock Climbing and Differential Equations: The Fall-Factor
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  1. Rock Climbing and Differential Equations: The Fall-Factor Dr. Dan Curtis Central Washington University

  2. Based on my article: “Taking a Whipper : The Fall-Factor Concept in Rock-Climbing” The College Mathematics Journal, v.36, no.2, March, 2005, pp. 135-140.

  3. Climbers use ropes and protection devices placed in the rock in order to minimize the consequences of a fall.

  4. Intuition says: The force exerted on the climber by the rope to stop a long fall would be greater than for a short fall.

  5. Intuition says: The force exerted on the climber by the rope to stop a long fall would be greater than for a short fall. • According to the lore of climbing, this need not be so.

  6. protection point climber belayer

  7. protection point climber belayer

  8. protection point climber belayer

  9. L = un-stretched length of rope between climber and belayer.

  10. DF DT

  11. The Fall-Factor is defined as the ratio DT / L

  12. The Fall-Factor is defined as the ratio DT / L Climbing folklore says: The maximum force exerted by the rope on the climber is not a function of the distance fallen, but rather, depends on the fall-factor.

  13. Fall-factor about 2/3

  14. Fall-factor 2 belay point

  15. position at start of fall 0 position at end of free-fall DF position at end of fall DT x

  16. During free-fall

  17. During free-fall

  18. During free-fall

  19. During free-fall

  20. when so

  21. when so

  22. when so When

  23. when so When After the rope becomes taut, the differential equation changes, since the rope is now exerting a force.

  24. The solution is

  25. Maximum force felt by the climber occurs when and

  26. Maximum force felt by the climber occurs when and

  27. The maximum force is given by