Answers

  1. If the system is disturbed, which way will the pulley turn as the chain falls? It might turn either direction depending on the exact starting position. There's always a bit of friction, otherwise we'd never be able to cause this sytem to be at rest, and the direction of that force due to friction will determine which way it turns when the friction is removed. The important point here is that in the position shown there's no greater likelihood of motion in one direction than the other.

  2. How can the weight be larger on the left and the chain still be in static equilibrium? Do a complete force and torque analysis. The suspended portions of the chain are analyzed in the same way we did for the overbalanced chain. The lever arm for one arm is 1.5 cm. The lever arm for the other is 3 cm. Therefore, without friction, the balance point would be with one side of the chain weighing twice that of the other. This fact gives a clue which way the friction is acting to prevent this chain's motion.

  3. Why do the suspended dice chains lean toward the right? Do the force analysis. They lean until the net torque on each hanging segment becomes zero. For example, on the left side, the leaning will be such that the center of mass of the suspended portion will be directly below the point of application of the upward force, at the radius of 1.5 cm. That point is the upper right corner of the die with its "3" face showing.

  4. Why doesn't the upper pulley need teeth to pull the chain up and over the pulley? Since the chain never moves, it never goes up and over the pulley. Also, if the chain did move, it would not be the pulley that lifts it, for the pulley has no input source of power. If, as the inventor assumes, the chain itself is the source of the power, the chain would move over the smooth pulley by itself. In fact, the little chain-of-dice demo shows that a ball-bearing low friction pulley supports unbalanced weight quite nicely.

Return to the the overbalanced chain problem.
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