Give Me a Place to Stand — Archimedes and the Earth
Archimedes is supposed to have said that with a place to stand he could move the Earth. The law of the lever has no upper limit written into it, so he was right: F₁d₁ = F₂d₂ will balance a 700 N man against a planet weighing 5.86 × 10²⁵ N, provided he stands 8.4 × 10²² m from the fulcrum — further away than the Andromeda galaxy. Slide him out along the beam and watch the distance climb past the Moon, the Sun and the Milky Way.
Cara memakai simulasi ini
- Slide the man out along the beam and watch the moments approach each other
- Change his weight and see the balance point move to compensate
- Follow the distance markers past the Moon, the Sun, the galaxy and beyond
- Use the camera bar to look at the fulcrum or fly out along the beam
Yang perlu diamati
- The beam is drawn on a logarithmic axis — twenty-two decades will not fit any other way
- Balance is reached at 8.4 × 10²² m, past the Andromeda galaxy
- Doubling the man's weight halves the arm he needs, exactly as F₁d₁ = F₂d₂ says
- Raising the Earth by one millimetre costs him a walk of 8.4 × 10¹⁹ m
- The law of the lever sets no upper limit — only the universe does
Fisika di baliknya
A lever balances when the two moments about the fulcrum are equal: F₁d₁ = F₂d₂. Nothing in that statement caps either quantity, so any force at all can balance any other if it is applied far enough out. The price is distance, and it is paid twice over: to raise the far load by a height h, the near end has to travel h × (d₁/d₂). Balancing the Earth needs an arm of 8.4 × 10²² m, and lifting it by a single millimetre means walking 8.4 × 10¹⁹ m — about nine thousand light years. The law is not wrong; it is simply indifferent to whether the arm it demands could exist.