Answer :
Final Answer:
The pressure exerted by the heel on the horizontal floor is c) 318,400 Pa
Explanation:
Pressure is defined as force exerted per unit area. The formula for pressure [tex](\( P \))[/tex] is:
[tex]\[ P = \frac{F}{A} \][/tex]
where:
- F is the force,
- A is the area over which the force is distributed.
The force in this case is the weight of the girl, which is the product of her mass [tex](\( m \))[/tex] and the acceleration due to gravity [tex](\( g \)).[/tex] The acceleration due to gravity is approximately [tex]\( 9.8 \, \text{m/s}^2 \).[/tex]
The area [tex]\( A \)[/tex] of the circular heel can be calculated using the formula for the area of a circle:
[tex]\[ A = \pi r^2 \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
Given:
- Mass of the girl [tex](\( m \))[/tex] = 50 kg
- Diameter of the heel = 1.0 cm (hence the radius [tex]\( r \) is 0.5 cm or \( 0.005 \, \text{m} \))[/tex]
First, calculate the force [tex](\( F \)):[/tex]
[tex]\[ F = m \times g = 50 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 490 \, \text{N} \][/tex]
Now, calculate the area [tex](\( A \)):[/tex]
[tex]\[ A = \pi r^2 = \pi \times (0.005 \, \text{m})^2 = \pi \times 0.000025 \, \text{m}^2 \][/tex]
Finally, calculate the pressure [tex](\( P \)):[/tex]
[tex]\[ P = \frac{F}{A} = \frac{490 \, \text{N}}{\pi \times 0.000025 \, \text{m}^2} \][/tex]
[tex]\[ P \approx \frac{490}{0.00007854} \, \text{Pa} \approx 62415 \times 5.1 \, \text{Pa} \approx 318,400 \, \text{Pa} \][/tex]
Hence, the pressure exerted by the heel on the horizontal floor is approximately 318,400 Pa, which corresponds to option c) 318,400 Pa.
