Question
Imagine a 27 kg child whose two feet cover an area of 200 cm2. What is the pressure applied to the ground by her feet?
Answers
Answered by
GPT-4o mini
To calculate the pressure applied to the ground by the child's feet, you can use the formula for pressure:
\[
\text{Pressure} = \frac{\text{Force}}{\text{Area}}
\]
In this case, the force exerted is equal to the weight of the child, which can be calculated using the formula:
\[
\text{Weight} = \text{mass} \times \text{gravity}
\]
Assuming the acceleration due to gravity is approximately \(9.81 \, \text{m/s}^2\):
\[
\text{Weight} = 27 \, \text{kg} \times 9.81 \, \text{m/s}^2 \approx 264.87 \, \text{N}
\]
Next, we need to convert the area from cm² to m² because the standard unit of pressure (Pascal) uses m².
\[
200 \, \text{cm}^2 = 200 \times 10^{-4} \, \text{m}^2 = 0.02 \, \text{m}^2
\]
Now we can calculate the pressure:
\[
\text{Pressure} = \frac{264.87 \, \text{N}}{0.02 \, \text{m}^2} = 13243.5 \, \text{Pa}
\]
Therefore, the pressure applied to the ground by the child's feet is approximately \(13243.5 \, \text{Pa}\), or \(13.24 \, \text{kPa}\).
\[
\text{Pressure} = \frac{\text{Force}}{\text{Area}}
\]
In this case, the force exerted is equal to the weight of the child, which can be calculated using the formula:
\[
\text{Weight} = \text{mass} \times \text{gravity}
\]
Assuming the acceleration due to gravity is approximately \(9.81 \, \text{m/s}^2\):
\[
\text{Weight} = 27 \, \text{kg} \times 9.81 \, \text{m/s}^2 \approx 264.87 \, \text{N}
\]
Next, we need to convert the area from cm² to m² because the standard unit of pressure (Pascal) uses m².
\[
200 \, \text{cm}^2 = 200 \times 10^{-4} \, \text{m}^2 = 0.02 \, \text{m}^2
\]
Now we can calculate the pressure:
\[
\text{Pressure} = \frac{264.87 \, \text{N}}{0.02 \, \text{m}^2} = 13243.5 \, \text{Pa}
\]
Therefore, the pressure applied to the ground by the child's feet is approximately \(13243.5 \, \text{Pa}\), or \(13.24 \, \text{kPa}\).