Question

Part 1: How much pressure is applied to the ground by a 50 kg man who is standing on square stilts that measure 0.04 m on each edge? Answer in units of Pa.

Part 2: What is this pressure in pounds per square inch? Answer in units of lb/in2.

Answer 1

To solve this problem, we will calculate the pressure exerted by the man on the ground. Pressure is defined as force per unit area.

### Part 1: Pressure in Pascals (Pa)

**Step 1: Calculate the man's weight.**
Weight (force due to gravity) can be calculated using the formula:
\[
\text{Weight} = \text{mass} \times \text{gravity}
\]
Assuming the acceleration due to gravity is approximately \(9.81 \, \text{m/s}^2\):
\[
\text{Weight} = 50 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 490.5 \, \text{N}
\]

**Step 2: Calculate the area of one stilt.**
Each square stilt has a side length of \(0.04 \, \text{m}\):
\[
\text{Area} = \text{side}^2 = (0.04 \, \text{m})^2 = 0.0016 \, \text{m}^2
\]

**Step 3: Calculate pressure.**
Since the man is standing on square stilts, and if we assume he is standing on one stilt, the pressure is calculated as:
\[
\text{Pressure} = \frac{\text{Weight}}{\text{Area}} = \frac{490.5 \, \text{N}}{0.0016 \, \text{m}^2} = 306562.5 \, \text{Pa}
\]
Thus, the pressure applied to the ground by the 50 kg man standing on one stilt is:
\[
\text{Pressure} \approx 306562.5 \, \text{Pa}
\]

### Part 2: Pressure in pounds per square inch (lb/in²)

**Step 1: Convert Pascals to pounds per square inch.**
1 Pascal is equal to \(0.00014503773773 \, \text{lb/in}^2\). Therefore, to convert from Pascals to \( \text{lb/in}^2 \), we use:
\[
\text{Pressure in lb/in}^2 = \text{Pressure in Pa} \times 0.00014503773773 \, \text{lb/in}^2
\]
Calculating:
\[
\text{Pressure in lb/in}^2 = 306562.5 \, \text{Pa} \times 0.00014503773773 \, \text{lb/in}^2 \approx 44.466 \, \text{lb/in}^2
\]

### Summary of Results
- **Part 1:** The pressure exerted by the man is approximately **306562.5 Pa**.
- **Part 2:** The pressure exerted by the man is approximately **44.466 lb/in²**.