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Practice: Pressure Calculations

January 15, 2025
2 min read
practice math physics

Formula Review

P=FAP = \frac{F}{A}

Problem 1: The High Heels vs. Flat Shoes

A girl weighs 500 N500 \text{ N}.

  1. Case A: She wears flat shoes with a total sole area of 0.05 m20.05 \text{ m}^2.
  2. Case B: She wears high heels where the weight is concentrated on a heel area of just 0.001 m20.001 \text{ m}^2 (assume she stands on one heel for a moment).

Calculate the pressure in both cases.

Click to Reveal Solution

Case A (Flats): P=5000.05=5005/100=500×20=10,000 PaP = \frac{500}{0.05} = \frac{500}{5/100} = 500 \times 20 = \mathbf{10,000 \text{ Pa}}

Case B (Heels): P=5000.001=5001/1000=500×1000=500,000 PaP = \frac{500}{0.001} = \frac{500}{1/1000} = 500 \times 1000 = \mathbf{500,000 \text{ Pa}}

Observation: The heels exert 50 times more pressure! This is why heels sink into grass.

Problem 2: The Brick

A brick has dimensions 20 cm×10 cm×5 cm20 \text{ cm} \times 10 \text{ cm} \times 5 \text{ cm} and weighs 20 N20 \text{ N}. Calculate the maximum and minimum pressure it can exert on the ground.

Hint: Max pressure occurs on the smallest area. Min pressure occurs on the largest area.

Click to Reveal Solution

Step 1: Calculate Areas (convert to meters!)

  • Face 1 (20×1020 \times 10): 0.2×0.1=0.02 m20.2 \times 0.1 = 0.02 \text{ m}^2
  • Face 2 (20×520 \times 5): 0.2×0.05=0.01 m20.2 \times 0.05 = 0.01 \text{ m}^2 (Smallest Area)
  • Face 3 (10×510 \times 5): 0.1×0.05=0.005 m20.1 \times 0.05 = 0.005 \text{ m}^2 … Wait.
    • 20×10=200 cm220 \times 10 = 200 \text{ cm}^2
    • 20×5=100 cm220 \times 5 = 100 \text{ cm}^2
    • 10×5=50 cm210 \times 5 = 50 \text{ cm}^2 (Smallest Area is actually this one).

Correction:

  • Largest Area (20×1020 \times 10): 0.02 m20.02 \text{ m}^2.
  • Smallest Area (10×510 \times 5): 0.005 m20.005 \text{ m}^2.

Step 2: Calculate Pressure

  • Minimum Pressure (Largest Area): P=200.02=1000 PaP = \frac{20}{0.02} = \mathbf{1000 \text{ Pa}}
  • Maximum Pressure (Smallest Area): P=200.005=4000 PaP = \frac{20}{0.005} = \mathbf{4000 \text{ Pa}}