Ask A Scientist Physics Archive

name         Dave M.
status       other
age          50s

Question -   I am a rock climber; equipment specifications are in kilo
newtons.  So, if 175 lb. climber falls 10 ft. and is stopped by a piece
of climbing gear; how much force is this?  Example: a carabinner is rated
at 20KN; how far can a 175lb. climber fall an still expect the carabinner
to not fail/break?
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Dave,
There is no specific answer.  The force required to stop the climber depends
very much on how much the cable can stretch.  As for weight of the climber,
2 pounds is about 9 Newtons.  Our climber weighs about 800 Newtons, or 0.8
KN.  To just support the climber hanging freely, the rope must supply 0.8 KN
of force.

When the climber falls, the rope needs the 0.8 KN to counter his weight PLUS
the force required to bring him to a halt.  Ten feet is about 3 meters.  The
amount of energy gained by the climber as he falls is (0.8KN)(3m)=2.4 KN.m =
2.4 kiloJoules.  The maximum force the rope can exert is 20KN.  Since the
climber weighs 0.8KN, a maximum of about 19KN can be devoted to slowing the
climber.  From no stretch to maximum stretch, the average force is about 9.5
KN.  Multiply this by how much 20 KN stretches the rope.  A stretch of about
0.25 meters (9inches) can absorb the 2.4 kiloJoules of energy.  More stretch
will work better.  More stretch means less force is required to stop the
climber.  If the 20 KN produces a stretch of only 0.1 meter, the rope can
only absorb about
(9.5KN)(0.1m)=0.95KJ.  This would not be enough.  This is why long ropes
hanging from far above are preferred.  A long rope can stretch more.

Dr. Ken Mellendorf
Physics Instructor
Illinois Central College
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