To find the RNA (radius of the new axle), we'll start by converting the width of the tire and the rim diameter into the same unit.
Given:
Wheel speed (RPM) = 1125.56 RPM
Speed (km/h) = 120 km/h
Width of the tire (mm) = 175 mm
Rim diameter (inches) = 14 inches
Now, let's convert the width of the tire from millimeters to inches. Since there are 25.4 mm in an inch, the width of the tire in inches is:
Width of the tire (inches) = 175 mm / 25.4 ≈ 6.89 inches
Next, let's find the circumference of the tire. The circumference is given by:
Circumference (inches) = π × diameter
The diameter of the tire is calculated as the sum of the rim diameter and twice the width of the tire:
Diameter (inches) = Rim diameter (inches) + 2 × Width of the tire (inches)
= 14 inches + 2 × 6.89 inches
= 14 inches + 13.78 inches
= 27.78 inches
Now, we can find the circumference of the tire:
Circumference (inches) = π × 27.78 inches
= 87.15π inches
To find the RNA, we'll use the formula:
RNA = Speed (km/h) × 1000 m/km × 1 h/3600 s ÷ (2π × Wheel speed (RPM) × Circumference (m))
Let's convert the speed from km/h to m/s:
Speed (m/s) = 120 km/h × 1000 m/km × 1 h/3600 s
= 33.33 m/s
Now, let's calculate the RNA:
RNA = 33.33 m/s ÷ (2π × 1125.56 RPM × (87.15π inches × 0.0254 m/inch))
≈ 33.33 m/s ÷ (2π × 1125.56 RPM × 2.2113 m)
≈ 33.33 m/s ÷ (2π × 1125.56 RPM × 2.2113 m)
≈ 0.0047 m
Therefore, the RNA (radius of the new axle) is approximately 0.0047 m.