You are concerned about the moon roof on your new sports car. It seems to flex when driving at high speeds. Calculate how much net force the moon roof must withstand and in what direction. Assume the moon roof is flat with an area of 0.5 m^2 and the pressure and velocity over the moon roof is constant. Your driving speed is 20 m/s, and the velocity over the moon roof is 30 m/s. The pressure inside the car is 90,500 N/m^2 and the freestream pressure and density in front of the car are 90,000 N/m^2 and 1.1 kg/m^3.

Explanation:

We shall apply Bernoulli's formula to solve the problem . It is as follows .

P + ρ gh + 1/2 ρ v² = constant .

P₁ + ρ gh + 1/2 ρ v₁²  = P₂ + ρ gh + 1/2 ρ v₂²

P₁ +  1/2 ρ v₁²  = P₂  + 1/2 ρ v₂²

P₁ - P₂ = 1/2 ρ (v₂² - v₁² )

= .5 x 1,1 ( 30² - 20² )

= 275 N / m²

velocity over moon roof is high , pressure will be lower there by 275 N / m²

Given pressure difference already existing = 90500 - 90000 = 500 N / m²

Additional pressure difference due to velocity difference = 275 N / m²

Total pressure difference = 275 + 500 = 775 N / m²

Area of roof = .5 m²

Total force acting upwards on the roof

= .5 x 775 N

= 387.5 N .

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