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Torsion Physics

  1. Jan 3, 2008 #1
    Is anyone familiar with a rope skein like on a torsion catapult? Essentially there are two points between which a great length of rope is wound. The base of an arm is placed in the center of this oblong before both of the fixed points are twisted in the same direction. This process forces the arm in that direction too, but a brace stops it perpendicular to the base. The arm is pulled back, loaded, and released. The elastic potential in the rope combined with a 3rd class lever gives the projectile its force. There are a few more interesting aspects to the device as a whole, but my questions are concerning the skein itself.

    I logically assume that there must be a functional ratio between the torque force in the rope and the normal force exerted by the frame on the "two points" between which the skein is wound. For simplicity, let's assume these points are wooden dowels. It's easy to tell that the friction builds up as the rope is wound due to the increasing normal force (the precise amount dependent on the coefficient of friction between the two surfaces). Initially the frictional force is greater than the torsion force and so it does not unwind. My question is this: will the friction continue to hold indefinitely, or will it eventually not be enough? What is the math that describes this relationship?

    I also have another question, though probably much simpler. Imagine that those dowels were attached to large 14" diameter sprockets like on an over-sized bike. A strong chain connects them to smaller 5" diameter sprockets that could be turned with a 6' long wrench. The idea is to achieve the best possible mechanical advantage. What is the ratio between the breaking strength of the chain and the maximum possible force stored in the skein?

  2. jcsd
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