Final answer:
The force on the sail can be calculated using Bernoulli's principle by relating wind velocity to pressure differences and considering air density. Multiplying the pressure difference with the sail area gives the force on the sail. The effectiveness of this force for propelling a sailboat depends on its capacity to move the boat against resistances.
Step-by-step explanation:
Force Calculation on a Sail
To calculate the force exerted on a square meter of sail by the wind, we can use Bernoulli's principle, which relates the pressure difference to the velocity difference. Given the horizontal velocities of wind on the front (6.00 m/s) and back surfaces (3.50 m/s) of the sail and the density of air (1.29 kg/m³), we can calculate the force on the sail as follows.
First, we use the Bernoulli equation to find the pressure difference:
P1 + ½ρv1² = P2 + ½ρv2²
Making P1 - P2 the subject of the formula and substituting the given velocities (v1 and v2) and the density (ρ), we find the pressure difference. The force can be found by multiplying this pressure difference by the sail area (1 m²).
Discussing the effectiveness of the force for propelling a sailboat involves considering whether the calculated force is sufficient to move the boat against various resistances such as water drag and boat weight. If the force is significant, it can indeed propel the sailboat effectively.