Stevin's Wreath of Spheres
Simon Stevin argued about equilibrium on inclined planes in 1586, a century before Newton's laws, and he did it with a picture rather than an equation. A closed loop of identical spheres is draped over a wedge with two slopes of different steepness. The long, shallow side carries more spheres; the short, steep side pulls harder on each one. Tilt the wedge as far as you like, then release the wreath and watch nothing happen.
इस सिमुलेशन का उपयोग कैसे करें
- Slide the apex along the base to make one slope shallow and the other steep
- Press Release the wreath to let it slide freely and see whether it moves
- Use the camera bar for the whole figure or a close look at the apex
क्या देखें
- The shallow slope holds more spheres, in the ratio of the two slope lengths
- Each sphere on the steep slope pulls harder along its own slope
- The product — the pull on each side — comes out the same at every tilt
- Released, the wreath does not creep round, however unequal the two slopes look
- The hanging festoon stays symmetrical, so it pulls the two base corners equally
- The wreath keeps its length: the festoon takes up whatever the slopes do not
इसके पीछे की भौतिकी
A slope of angle θ rising to a height h has length h / sin θ, so the weight of chain lying on it is proportional to 1 / sin θ. The share of that weight acting along the slope is sin θ. Multiplying the two, the sine cancels and each slope pulls the wreath with the same λ g h, where λ is the mass per unit length. The festoon hanging underneath is a catenary between two points at the same height, so it is symmetrical and pulls the two corners equally — cutting it away changes nothing, which is the step that makes the argument work. Stevin's reason for trusting the conclusion without equations was the consequence of the alternative: if one side did win, the wreath would creep round, and after a full turn every sphere would be back where it started with the chain still moving. That is perpetual motion, so the effects must be equal.