A girl is wearing a pair of flat shoes. She weight 550 N. The area of contact of one shoe with the ground is `160 cm ^(2)`.What pressure will be exerted by the girl on the ground if she stands on two feet ?

Answer

To solve the problem of calculating the pressure exerted by the girl on the ground when she stands on two feet, we will follow these steps:

### Step 1: Understand the Given Information
- The weight of the girl (W) = 550 N
- The area of contact of one shoe with the ground (A) = 160 cm²

### Step 2: Convert the Area from cm² to m²
To use the area in standard SI units, we need to convert it from cm² to m²:
\[ A = 160 \, \text{cm}^2 = 160 \times 10^{-4} \, \text{m}^2 = 0.016 \, \text{m}^2 \]

### Step 3: Calculate the Total Area of Contact for Two Feet
Since the girl is standing on two feet, the total area of contact (A_total) will be:
\[ A_{\text{total}} = 2 \times A = 2 \times 0.016 \, \text{m}^2 = 0.032 \, \text{m}^2 \]

### Step 4: Calculate the Pressure Exerted
Pressure (P) is defined as the force (weight of the girl) divided by the area of contact:
\[ P = \frac{W}{A_{\text{total}}} \]
Substituting the values we have:
\[ P = \frac{550 \, \text{N}}{0.032 \, \text{m}^2} \]

### Step 5: Perform the Calculation
Calculating the pressure:
\[ P = \frac{550}{0.032} \approx 17187.5 \, \text{N/m}^2 \]

### Step 6: Final Answer
Thus, the pressure exerted by the girl on the ground when she stands on two feet is approximately:
\[ P \approx 17187.5 \, \text{N/m}^2 \]