Final answer:
The force on a square meter of sail, based on Bernoulli's principle with given velocities and air density, is approximately 14.0575 Newtons.
Step-by-step explanation:
To calculate the force on a square meter of sail, we can apply Bernoulli's principle, which relates the wind velocity to pressure differences. First, we need the difference in wind velocities on both sides of the sail. The wind has a velocity of 6.11 m/s on the front surface and 3.94 m/s on the back surface of the sail. The air density (ρ) is given as 1.29 kg/m³.
The Bernoulli equation is given by P + 0.5 ρv² = constant, where P is the pressure and v is the velocity of the fluid (air in this case). For each side of the sail, we have P1 + 0.5 ρv1² = P2 + 0.5 ρv2². Since the pressures P1 and P2 are the pressures on the front and back of the sail, we can find the difference in pressure (ΔP) and then use it to calculate the force (F) exerted on the sail by the wind as F = ΔP × area. Here, the area (A) is 1 square meter.
ΔP = 0.5 ρ(v1² - v2²)
= 0.5 × 1.29 kg/m³ × ((6.11 m/s)² - (3.94 m/s)²)
= 0.5 × 1.29 kg/m³ × (37.3321 m²/s² - 15.5236 m²/s²)
= 0.5 × 1.29 kg/m³ × 21.8085 m²/s²
= 14.0575 N/m²
The force on the sail is then F = ΔP × A = 14.0575 N/m² × 1 m² = 14.0575 N.