### Re: What force is seen at the end of a rope with a load of a 200 lb man?

Date: Mon Jun 5 04:22:13 2000
Posted By: Bruno Putzeys, Staff, Electrpacoustics and Analog Electronics, Philips ITCL
Area of science: Engineering
ID: 954272823.Eg
Message:
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You don't have enough information to determine this. As force (f) is
linked to the person's mass (m=100kg) and his acceleration (in this case
sudden deceleration caused by the rope being pulled taut) as f=m*a , the
deceleration is still missing. You'll guess that the deceleration will be
quite brusque and hence the force large as the rope won't stretch. The
"stretchiness" is called compliance (spring constant k) and is defined as
"meters of elongation per newton of force" (l/f).
Should you manage by measurement to determine the combined compliance of
the pole, the rope, the belt and the man's belly (the latter will
dominate) you could start reasoning as follows: a certain velocity (dx/dt)
and hence stretch rate will give rise, through the compliance, to an
increase of force versus time (df/dt). This in turn will cause
deceleration.
However, by the time velocity has decreased to 0 the force is subtantially
higher than the man's weight. The stretched system of rope+belt+fat will
start tugging upward again. By the time the force on the rope has
normalized again the velocity is no longer zero! If you've followed this
mathematically you'll find that the only solution to the resulting
differential equation involves a sinusoidal function with time.
This bouncing up and down is called "harmonic motion", some description of
which is available under  http://colleg
shown that the occasional falling telegraph pole serviceman does indeed
bob up and down a bit but not indefinitely. This is due to the fact that
the kinetic and potential energy represented by the velocity and force
respectively are lost (dissipated) due to braking (=turned into heat by
friction). This friction takes place in the rope and in the man's body
tissue.
Some practical examples will show how different the same system can behave
by changing some elements:
-The man on the rope: Will exert a force on the rope substantially higher
than his own weight (not equal to mass, mind you). His "spare tyre" will
limit this force to a reasonable limit and he will hardly rebound. The
exact force profile as you may guess is difficult to calculate as under
these circumstances the mechanical properties of the human body will
dominate the equation.
-A solid block of concrete, same mass (200lbs), same rope. The block will
not have any compliance, the rope won't either. Most probably the rope
will snap.
-The bungee-rope jumper. The compliance of the bungee-rope is very lare
and dominates. The deceleration will not be very large and the force will
be relatively small as well. This means that the human body will not be
effective in dissipating much of the energy and the person at the end of
the rope (a bundle of rubber bands really) will bob up and down quite a
lot.

That wouldn't have been a nice homework question, I daresay.

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