2 Enrichment: heel against elephant

• Which presses harder on the ground, an elephant's foot or a woman's pointed heel?
• Because the area of a pointed heel is tiny, the pressure under it can be much greater than under an elephant's broad foot, even though the elephant's weight is far larger.

Example 1. A 60 kg person stands on both feet, each of contact area 200 cm². (g = 9.8 m/s²) Weight = 60 × 9.8 = 588 N; total area = 400 cm² = 0.04 m². P = 588/0.04 = 14 700 N/m². Standing on one foot doubles the pressure to 29 400 N/m².

Example 2. A heel of area 1 cm² carries 300 N: P = 300/10⁻⁴ = 3 × 10⁶ N/m². A foot of area 0.04 m² carrying 5000 N gives only 1.25 × 10⁵ N/m².

Example 3 (a block). A solid block 4 cm × 10 cm × 25 cm has density 2500 kg/m³ (take g = 10 m/s²). Its volume is 1000 cm³ = 10⁻³ m³; mass = 2.5 kg; weight = 25 N.

• Largest pressure (smallest face 4 × 10 cm² = 4 × 10⁻³ m²): P = 25 / 4 × 10⁻³ = 6250 N/m².
• Smallest pressure (largest face 10 × 25 = 250 cm² = 0.025 m²): P = 25/0.025 = 1000 N/m².

Why do we use a sharp knife, and wide tracks on a tractor? Sharp edge → small area → large pressure (cuts easily). Wide tracks → large area → small pressure (does not sink in soft ground).