Perfect Balance

Why it matters

A 30 kg kid and a 60 kg adult CAN balance a see-saw — every playground proves it daily. The heavier side just has to sit smarter, not lighter.

The idea in plain words

The law every balance obeys. Tap the terms.

Σ anticlockwise moments = Σ clockwise moments

A metre rule balances at 50 cm. A 20 gf weight hangs at 20 cm. Where must 30 gf hang?

At the 70 cm mark

• both conditions: equilibrium — no net force AND no net moment — the body neither slides nor turns
• N·m: Σ acw — total of all moments turning anticlockwise about the pivot
• N·m: Σ cw — total of all moments turning clockwise — equal at balance
• acw: 20 gf × 30 cm = 600 gf·cm
• cw needed: 30 gf × d = 600 → d = 20 cm right of pivot

Predict first

A 5 N weight hangs 0.2 m left of the pivot. Which single weight balances it?

Balance is about MOMENTS, not weights: 5 × 0.2 = 1.0 N·m needs any combination giving 1.0 N·m — like 2 N × 0.5 m. ✓

• 2 N at 0.5 m on the right — correct
• Only another 5 N at 0.2 m
• Nothing lighter than 5 N can do it

What you do

A 5 N weight is stuck at 0.2 m on the left. Balance the beam using ONLY 1 N and 2 N weights on the right hooks.

Check yourself

A beam balances with 4 N at 0.3 m left and 6 N at distance d right. d = ?

4 × 0.3 = 1.2 = 6 × d → d = 0.2 m. The heavier weight sits closer.

For a body in equilibrium under several forces…

Cancel forces but not moments → it spins. Cancel moments but not forces → it slides. Equilibrium needs both.

The see-saw taught you that a small child CAN lift a heavy adult by…

Moment = weight × distance. Distance is the child's lever — Archimedes' 'place to stand' in playground form.

• 0.2 m — correct
• 0.45 m
• 0.3 m
• both the resultant force and the resultant moment are zero — correct
• only the forces need to cancel
• only the moments need to cancel
• sitting farther from the pivot — correct
• bouncing
• it's impossible