Answer to Question #184389 in Mechanics | Relativity for Konoha

Question

Calculate the approximate force on a square meter of sail, given the horizontal velocity of the wind is 9.16 m/s parallel to its front surface and 4.9 m/s along its back surface. Take the density of air to be 1.29 kg/m³.

Round your answer to 2 decimal places

Answer 1

$\text{force per square meter is the definition of pressure}$.

$\text{the pressure on the sail will be the difference in pressure}\newline \text{ on the inside and outside of the sail}$

$\text{according to bernoulli law:}$

$\frac{\rho v^2}{2}+\rho gh+P= const$

$\text {for front surface:}$

$\frac{\rho*9.16^2}{2}+\rho gh+P_1$

$\text {for back surface:}$

$\frac{\rho*4.9^2}{2}+\rho gh+P_2$

$\frac{\rho*9.16^2}{2}+\rho gh+P_1 =\frac{\rho*4.9^2}{2}+\rho gh+P_2$

$P_2-P_1=\frac{\rho*9.16^2}{2}-\frac{\rho*4.9^2}{2}=\frac{1.29*(9.16^2-4.9^2)}{2}\approx29.95$

$\text{Answer: }29.95$