|MadSci Network: Engineering|
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 estudent.infoplease.com/ce5/CE022919.html . 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 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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