Lever Balance Calculator
A lever balances when the turning effects cancel: each mass multiplied by its distance from the pivot, added up with sign, coming to zero. Distance counts as much as mass, which is why a child can balance an adult on a seesaw by sitting far enough back. This generates a set of weights, solves the last one's position so the lever balances exactly, and shows every moment so the cancellation is visible.
What this generator does
Places weights at random masses and distances on alternating sides of a pivot, then solves algebraically for where the final weight must sit so that the total moment is zero. It shows every mass, position and moment so the cancellation can be checked by eye as well as by the tool.
How to use this tool
- Choose how many weights to place on the lever.
- Read each mass and its signed distance — negative is left of the pivot, positive is right.
- Check the moment column: mass times position, summing to zero.
- Try working out the last position yourself before generating a new one.
Understanding the controls
- How many weights
- Between 2 and 5. All but the last are placed at random, and the last one's position is solved so the lever balances.
- Seed
- Any word reproduces exactly the same masses and positions, so a problem can be set and marked later.
Common use cases
- Physics practice on the principle of moments with checked answers
- Seesaw and balance-beam classroom problems
- Showing that distance and mass trade off exactly
- Generating worked examples with the arithmetic already verified
- Setting the same problem twice from a seed
How this generator works
The moment of a weight is its mass times its signed distance from the pivot, so a weight on the left contributes a negative moment and one on the right a positive one. Solving for the last position is a single division: the negative of everything else's total moment, divided by the last mass. The check recomputes the whole sum from the finished set of weights and requires it to be zero to within floating-point error.
Randomness and fairness
The masses and all but one position are random; the final position is a deterministic solution. A seed reproduces the same problem exactly and is therefore explicitly not cryptographically secure. Without a seed the browser's cryptographically secure generator is used.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- A weightless, rigid lever with a single fixed pivot — no beam mass and no bending.
- Positions are along one dimension only, so this covers seesaw-style problems rather than general statics.
- The solved position can land on either side and is not constrained to a tidy whole number.
- Gravity cancels out of the balance condition entirely, so masses are used directly rather than weights in newtons.
- Nothing is stored, so record the seed if the arrangement matters.
Privacy and your data
The problem and its solution are computed in your browser. Nothing about the weights or your seed is transmitted or kept.
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