Final answer:
The question is about calculating the force on a sail due to the wind using Bernoulli's principle. The wind velocity varies on different sides of the sail, and this pressure difference is used to find the force on a one square meter area of the sail.
Step-by-step explanation:
The question involves calculating the force on a sail based on the difference in wind velocity using Bernoulli's principle. We are given that the horizontal velocity of the wind along the front surface of the sail is 5.7 m/s, while it is 3.5 m/s along the back surface.
We also assume the air density to be 1.29 kg/m³. To calculate the force exerted by the wind on a sail, we can use Bernoulli's equation which relates the wind speed to pressure. According to Bernoulli's principle, the pressure difference between two points in a fluid flow is related to the difference in the fluid's velocity at those points. The greater the speed of the fluid, the lower the pressure.
Here's the calculation step-by-step:
- Calculate the wind pressure on the front surface (P1) using the wind velocity (V1 = 5.7 m/s).
- Calculate the wind pressure on the back surface (P2) using the wind velocity (V2 = 3.5 m/s).
- The force exerted by the wind on one square meter of sail can be found by the pressure difference: Force = (P1 - P2) × Area of sail
- Substitute the values and the density of air to get the approximate force on the sail.
To discuss if this force is effective for propelling a sailboat, we would compare the calculated force to the resistance forces acting on the boat, such as drag from the water and friction.