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.
Como usar esta simulação
- 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
O que observar
- 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
A física por trás
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.