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[Phys-L] A force multiplier



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. The F2/F1 ratio is 6 when the angle is 5 degree.

We all know how to explain this mathematically, deriving the F2/F1=1/[2*sin(alpha)] equation.

And one does not need a car to experimentally verify this theoretical expectation. The only instruments needed are two pulleys, hanging weights and a large protractor. Unfortunately, I never verified this counterintuitive relation. How close are the experimental and the theoretical F1/F2 ratios? If not very close then why?

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