Re: [Phys-L] A force multiplier

[Ludwik Kowalski <kowalskil@mail.montclair.edu>]

On Feb 9, 2013, at 7:28 PM, Ludwik Kowalski wrote:

> "Nearly every introductory physics textbook has an illustration showing a car being pulled out of mud. One end of the rope is attached to the car's bumper while the other is attached to a tree, on the other side of the road. A man, standing in the middle of the road, pulls the rope upwards, with a force F1. The force exerted by the rope on the car, F2, turns out to be several times larger, than F1, depending on the angle between the road and the rope. ...  We all know how to explain this mathematically, deriving the
>
> F2/F1=1/[2*sin(alpha)] 

equation. Now I understand why the textbook advice is not practical, when an ordinary rope is used. Suppose the maximum force a person can pull is F1= 200 lb while the force needed to move the car from the mud is F2=4000 lb. The angle alpha, needed, when F2/F1=20, according to the above formula, is about 1.4 degrees. Suppose the original horizontal distance from the bumper to the middle of the road is 10 meters, and that the rope is originally not stretched. The man pulls it up. The needed 1.4 degree is reached when the middle of the rope is only 0.24 meters above the road. The distance to the car (along the rope) changes from 10 meters to 10.24 meters. Such 2.4 % change, in the length of the rope, is not large enough to generate the needed F2/F1 ratio. The "spring constant" of a typical rope, in other words, is not large enough to satisfy the theoretical formula. That formula, however, would be reliable if the rope were replaced by a thick steel cable, as indicated by John. D.

Unless the rope is sufficiently rigid, the F2/F1 ratio will be significantly  lower (often much lower)  that what is predicted by the above theoretical formula, as students could verify by performing the experiment I described several days ago. 

Ludwik Kowalski
http://csam.montclair.edu/~kowalski/life/intro.html

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