- Difficulty
- Beginner
- Build time
- 35-55 min
- Estimated cost
- $0-$5
- Age range
- 10-15
- Workspace
- A clear table about 90 cm wide
The finish line
What you will build
The empty beam balances within 5 degrees of level and correctly identifies equal versus unequal sample masses in five comparison trials.
Learning goals
- Identify how gravity forces from two sample masses produces beam angle showing comparison.
- Construct and explain a static force difference-to-angular deflection system.
- Measure how the sample mass difference changes performance.
- Diagnose losses caused by pivot friction and unequal cup mass.
Before you build
Materials, tools, and safety
Reuse-material cost: $0-$3 with reused materials. Supervision: Adult help recommended for sharp or heated tools.
Tools
- Ruler
- Pencil
- Scissors
- Masking tape
Low-cost swaps
- Use clean recycled packaging whenever it has similar stiffness.
- Substitute paper clips, binder clips, or twist ties for specialty fasteners.
- Use two identical reusable containers and dry beans as reference masses.
Project-specific safety
- Wear eye protection when stretched elastic, magnets, or spinning parts are present.
- Test at floor or tabletop height and keep the path clear of people.
- Keep loads light, cover sharp skewer ends, and catch falling samples in a tray.
Orient the build
Place the build so gravity forces from two sample masses is on your left and beam angle showing comparison is on your right. Call the side facing you the front, the far side the back, the tabletop the bottom, and the opposite face the top.
Build it
Step-by-step instructions
Step 1
Build the stable stand
Brace two vertical supports around the pivot height.
Add a wide base that does not rock.
Step 2
Find the beam center
Measure and mark the midpoint, then make one centered pivot hole.
Check equal arm lengths to cup points.
Step 3
Hang the empty beam
Support it on a low-friction pivot and add a pointer at center.
Observe which side drops before adding cups.
Builder checkpoint: After hang the empty beam, the first subassembly should stay aligned when handled gently.
Step 4
Make matched cup hangers
Punch equal holes in identical cups and attach equal string loops.
Hang them at matching beam marks.
Watch for: If this stage binds or drifts, inspect beam flex before adding more parts.
Step 5
Zero the balance
Trim string or add tiny paper tabs until empty cups settle level.
Mark the zero pointer position.
Step 6
Calibrate with equal masses
Place five equal washers in each cup and wait for settling.
Confirm the pointer returns near zero.
Builder checkpoint: After calibrate with equal masses, operate the build slowly and confirm that beam angle showing comparison begins without binding.
Step 7
Run comparison trials
Hide different washer counts and predict heavier, lighter, or equal.
Record five outcomes.
Step 8
Explore arm length
Move one cup inward while keeping masses equal.
Explain the new imbalance using moments.
Builder checkpoint: At the final checkpoint, The empty beam balances within 5 degrees of level and correctly identifies equal versus unequal sample masses in five comparison trials.
See the engineering
Why it works
- Input
- gravity forces from two sample masses
- Output
- beam angle showing comparison
- Motion
- static force difference-to-angular deflection
- Energy losses
- pivot friction, unequal cup mass, off-center strings, beam flex
Why this works
Rotational equilibrium
A beam balances when clockwise and counterclockwise moments about the pivot are equal. Equal arm lengths make equal mass the level condition.
Look for: Move the same mass closer to the center and watch its turning effect decrease.
Where the energy goes
Efficiency and losses
The ideal model leaves out pivot friction, unequal cup mass, off-center strings, beam flex. These effects turn some input energy into heat, sound, vibration, or unwanted motion, so measured performance will be lower than an ideal calculation.
Look for: Run the build slowly and locate the first place where pivot friction becomes visible or audible.
Math bite
Balance unequal distances
Formula: mass₁ × distance₁ = mass₂ × distance₂
- Mass₁ = 40 g at 10 cm
- Distance₂ = 20 cm
Substitute: mass₂ = 40 × 10/20 = 20 g
Result: Twenty grams at 20 cm balances forty grams at 10 cm.
Distance can trade against force in moment equilibrium.
Pivot friction and beam mass affect precision.
Make it behave
Test, troubleshoot, and tune
Controlled test
Start here: Balance the two empty cups before comparing samples.
Success looks like: The pointer stays within 5 degrees of zero for equal masses and identifies all five comparisons correctly.
Measure: Pointer angle and correct comparison count.
Change: the sample mass difference
Keep constant: beam, arm lengths, cups, strings, stand, and settling time
- equal samples
- one-washer difference
- three-washer difference
| Symptom | Likely cause | Confirm it | Fix |
|---|---|---|---|
| The empty scale leans | Beam, strings, or cups are unequal | Swap cups between sides | Re-zero with matching parts |
| The beam sticks | Pivot friction is high | Tap lightly and watch whether it settles differently | Use a smoother centered pivot |
| Cups swing too long | Strings are long or test is disturbed | Wait and shield from airflow | Shorten equal strings |
| Results change after moving cups | Distances are no longer equal | Measure pivot-to-string centers | Reset symmetric marks |
Choose your tradeoff
A low-friction pivot improves sensitivity but also increases swinging. Use equal lightweight cups, measure from the pivot center, and allow consistent settling time.
Keep experimenting
Try another version
Heavy-light sorter
Compare clearly different objects.
Smallest detectable difference
Find the minimum washer change that reliably moves the pointer.
Unequal-arm scale
Calibrate mass from known arm positions.
Build together
Classroom and access options
Classroom version
Teams can compare the sample mass difference while keeping beam, arm lengths, cups, strings, stand, and settling time. Assign builder, tester, recorder, and explainer roles; have each team predict the result before collecting three trials.
Access adaptations
- Offer pre-cut parts and tactile or high-contrast measurement marks.
- Split roles so one builder can hold, another assemble, and another measure.
- Add a long high-contrast pointer and tactile center and equal-arm marks.
Reflect on the design
- How did the sample mass difference change the measured result?
- Where did pivot friction affect the build most strongly?
- What evidence shows that rotational equilibrium explains the motion?
- Which change would improve beam angle showing comparison without creating a new problem?
Glossary
- Rotational equilibrium
- A beam balances when clockwise and counterclockwise moments about the pivot are equal.
- Input
- The action or energy supplied to a system; here it is gravity forces from two sample masses.
- Output
- The useful response produced by a system; here it is beam angle showing comparison.
- Efficiency
- The fraction of input energy that becomes useful output instead of friction, sound, heat, or unwanted motion.
Build your dreams
One build can start the next.
Share what you learned, change one variable, and help another builder understand what worked.
Explore more guidesSources and build notes
A familiar household engineering activity implemented with original instructions and controlled tests.
- Classroom engineering basis: A common educational challenge implemented with original dimensions, tests, diagrams, and instructions.
Written and edited by BrickLabClips. Published 2026-07-22; updated 2026-07-22.