MadSci Network: Engineering

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

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 
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 . Reality has 
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 
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 

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

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