Balancing the Ruler — Coins, Distance and the Product
A ruler laid across a pencil and a handful of identical coins: one coin far out will hold several stacked in close, and the ruler goes level the instant the two products match. Record each arrangement in the table, read the moments in coin·cm or in N·m, and watch the law Archimedes wrote down for the lever fall straight out of the numbers.
Bu simülasyon nasıl kullanılır
- Set the number of coins and their distance on each side of the pivot
- Press Let go to release the ruler and see which way it tips
- Press Balance the left pile for me to solve the arrangement automatically
- Load the Archimedes case — one coin at 14 cm holding twelve near the pivot
Nelere dikkat etmeli
- The ruler goes level exactly when the two products are equal, not the two counts
- Moving a coin twice as far out lets it hold twice as many on the other side
- With equal distances on both sides only the number of coins decides the tip
- One coin can balance a dozen, provided it sits far enough from the pivot
- The same balance condition reads identically whether you count coin·cm or newton·metres
Arkasındaki fizik
Each coin exerts a downward force at its own distance from the pivot, so its moment is that force times that distance. The ruler balances when the total clockwise moment equals the total anticlockwise moment. With identical coins the weights are all the same and cancel from both sides, leaving the condition in the countable form n₁d₁ = n₂d₂. Distance and number therefore trade off exactly against each other, which is the principle of the lever: a small force far from the pivot balances a large one close to it.