A 50 kg girl wearing high heel shoes balances on a single heel. The heel is circular with a diameter 1.0 cm. What is the pressure exerted by the heel on the horizontal floor?
The pressure exerted by the heel on the horizontal floor is approximately ⁶ Pa.
Explanation
This numerical problem is similar to Example 9.1 in the textbook, which calculates pressure using the formula P = F/A. The key steps involve calculating the weight of the girl as the force and determining the cross-sectional area of the circular heel. Using g = 10 m/s² (as done in Example 9.1), the force is 500 N. The area of the circular heel with diameter 1.0 cm (radius 0.5 cm = 0.005 m) is calculated using πr². The final pressure is obtained by dividing force by area.
Solution Steps
Step 1: Calculate the force acting on the heel. The girl balances on a single heel, so her entire weight acts on it. F = mg = 50 kg × 10 m/s² = 500 N (taking g = 10 m/s² as per Example 9.1).
Step 2: Calculate the area of the circular heel. Diameter = 1.0 cm, so radius r = 0.5 cm = 0.005 m. Area A = πr² = π × (0.005)² = π × ⁻⁶ m² = ⁻⁵ m² (taking π = 3.14).
Step 3: Calculate pressure using P = F/A. P = 500 N / (⁻⁵ m²) = ⁶ N m⁻² ⁶ Pa.