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Rock Climbing and Differential Equations: The Fall-Factor

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## Rock Climbing and Differential Equations: The Fall-Factor

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**Rock Climbing and Differential Equations: The Fall-Factor**Dr. Dan Curtis Central Washington University**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.**Climbers use ropes and protection devices placed in the rock**in order to minimize the consequences of a fall.**Intuition says:**The force exerted on the climber by the rope to stop a long fall would be greater than for a short fall.**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.**protection point**climber belayer**protection point**climber belayer**protection point**climber belayer**L = un-stretched length of rope**between climber and belayer.**DF**DT**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.**Fall-factor 2**belay point**position at start of fall**0 position at end of free-fall DF position at end of fall DT x**when**so**when**so**when**so When**when**so When After the rope becomes taut, the differential equation changes, since the rope is now exerting a force.