Test moment balance in a supervised ruler experiment
Plan a resting ruler balance, compare measured opposing moments and discuss uncertainty.
Extended only (Supplement); Physics 0625, 2026–2028, section 1.5.2. Extend the principle of moments to several forces and describe a supervised experiment testing the absence of a resultant moment in equilibrium. Use each force's perpendicular distance and check the resultant force separately. Written method exercises do not demonstrate practical competence.
Before you begin
- Calculate moments from known forces and distances.
- State force and moment equilibrium conditions.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
For a load at the 30 cm mark and pivot at 50 cm, what is its lever arm on a horizontal ruler?
What you will learn
- Describe an experiment checking zero resultant moment in equilibrium.
- Explain reference distances, repeats and practical limitations.
Choose a support and control its own turning effect
Under teacher supervision, support a uniform metre ruler at its measured balance point with a stable suitable pivot. In the ideal uniform example this is the 50 cm mark, where its own weight acts. Hang known total loads, including any hangers, on opposite sides. Adjust a load position until the ruler rests approximately horizontal, then measure perpendicular distances from the pivot to each vertical load line.
For original illustrative values, a 2.0 N load at 30 cm is 0.20 m left of the 50 cm pivot and a 1.0 N load at 90 cm is 0.40 m right. Opposing moments are 2.0 × 0.20 = 0.40 N m and 1.0 × 0.40 = 0.40 N m. Equal opposing sums support zero resultant moment in that resting model; the pivot reaction supplies vertical force balance.
Record evidence rather than claiming perfect apparatus
Repeat balances with several suitable load-distance pairs, record force and perpendicular distance for each, and compare clockwise with anticlockwise moment sums. If using masses, convert their total mass to weight with the stated common g, or use common-field mass-distance products for balance comparison. A ruler mark is a position, not automatically a distance from the pivot.
Allow for uncertainty in load values, distance readings, the actual balance point and friction at the pivot. Nearly equal measured products within their measurement uncertainty support the model; a single level-looking ruler does not prove exact equality to unlimited precision. Use only teacher-approved loads and stable apparatus, keep suspended loads clear, and do not infer performed practical competence from this written planning task.
Pause and explain
What should be compared to test no resultant moment in a resting balance?
Worked example
A uniform ruler rests about the 50 cm pivot with 2.0 N at 30 cm and 1.0 N at 90 cm. Compare its load moments.
Show the worked solution
- Perpendicular distances are (50 − 30)/100 = 0.20 m and (90 − 50)/100 = 0.40 m.
- Anticlockwise moment = 2.0 × 0.20 = 0.40 N m.
- Clockwise moment = 1.0 × 0.40 = 0.40 N m, supporting no resultant moment in the ideal model.
Answer 0.40 N m anticlockwise and 0.40 N m clockwise.
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
For pivot 50 cm, loads 2.0 N at 30 cm and 1.0 N at 90 cm, compare the opposing moments.
Give me a hint
Convert separations from the pivot rather than absolute positions.
Compare my reasoning
- Left distance = 0.20 m and right distance = 0.40 m.
- Left moment = 2.0 × 0.20 = 0.40 N m.
- Right moment = 1.0 × 0.40 = 0.40 N m.
0.40 N m on each side, in opposite directions.
Look for these in your work
- Use distances from the pivot.
- State opposing rather than adding directions.
With a uniform ruler pivot at 50 cm, a 3.0 N load hangs at 40 cm. Where should a 1.5 N load hang to its right for ideal balance?
Give me a hint
Find the missing distance before converting back to a ruler position.
Compare my reasoning
- Left distance = 0.10 m and moment = 3.0 × 0.10 = 0.30 N m.
- Right distance = 0.30/1.5 = 0.20 m or 20 cm.
- Right ruler position = 50 + 20 = 70 cm.
The 70 cm mark.
Look for these in your work
- Find the required lever arm.
- Convert that distance into a position from the same reference.
A measured experiment gives opposing moments 0.400 N m and 0.408 N m, each with stated uncertainty ±0.010 N m. Explain the evidence and suggest one improvement.
Give me a hint
Compare the mismatch with the supplied uncertainty ranges instead of claiming perfect equality.
Compare my reasoning
- The stated ranges 0.390–0.410 and 0.398–0.418 N m overlap.
- The measurements are compatible with balance within those uncertainties, not proof of exact equality.
- Repeat suitable balances and improve distance readings or check the pivot balance point.
Compatible with balance within the stated uncertainties; repeat and improve distance or balance-point measurements.
Look for these in your work
- Use the stated uncertainty evidence.
- Suggest a specific measurement improvement.
Common mistakes
- Subtract pivot position to find each lever arm.
- Include hanger force and the actual ruler balance point.
- Describe supervision and measurement uncertainty.
What can you explain now?
Would using the 30 cm mark as a 0.30 m distance from the 50 cm pivot be correct?
Compare with the explanation
No; the separation is 0.20 m.
A scale position must be compared with the pivot reference.
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Make it stick
Describe apparatus, reference distances, several balances and uncertainty for a supervised moment experiment.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.