# Rock Climbing and Differential Equations: The Fall-Factor - PowerPoint PPT Presentation

Rock Climbing and Differential Equations: The Fall-Factor

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Rock Climbing and Differential Equations: The Fall-Factor

## 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 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 2 belay point

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

15. During free-fall

16. During free-fall

17. During free-fall

18. During free-fall

19. when so

20. when so

21. when so When

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

23. The solution is

24. The maximum force is given by