To calculate the pressure exerted by each of these wheels, you can use the formula for pressure:
Pressure (P) = Force (F) / Area (A)
In this case, the force is equal to the weight of each wheel, which can be calculated as the mass (m) multiplied by the acceleration due to gravity (g):
F = m * g
Where:
- m is the mass of each wheel (50 kg)
- g is the acceleration due to gravity (approximately 9.81 m/s²)
Now, you need to calculate the area for each wheel. The area of a circle is given by:
A = π * r²
Where:
- π (pi) is approximately 3.14159
- r is the radius of each wheel in meters
Let's calculate the pressure for each wheel:
1. For the first wheel with a radius of 5 cm (0.05 meters):
A = π * (0.05 m)² = 0.007853 square meters
F = 50 kg * 9.81 m/s² ≈ 490.5 N (Newtons)
Pressure (P1) = F / A = 490.5 N / 0.007853 m² ≈ 62,401.6 Pascal (Pa)
2. For the second wheel with a radius of 10 cm (0.1 meters):
A = π * (0.1 m)² = 0.0314159 square meters
F = 50 kg * 9.81 m/s² ≈ 490.5 N (Newtons)
Pressure (P2) = F / A = 490.5 N / 0.0314159 m² ≈ 15,601.7 Pascal (Pa)
3. For the third wheel with a radius of 15 cm (0.15 meters):
A = π * (0.15 m)² = 0.0706858 square meters
F = 50 kg * 9.81 m/s² ≈ 490.5 N (Newtons)
Pressure (P3) = F / A = 490.5 N / 0.0706858 m² ≈ 6,946.9 Pascal (Pa)
So, the pressure exerted by each of these wheels is approximately:
- P1 ≈ 62,401.6 Pascal (Pa)
- P2 ≈ 15,601.7 Pascal (Pa)
- P3 ≈ 6,946.9 Pascal (Pa)