A hurricane strength wind is blowing at a speed of 100 km/hr over a flat square roof of 10 m per side.Assuming the inside of the house to be at 1 atm pressure and the density of air is 1.3 kg/m³,calculate the lifting force on the roof. A)5.0 $\times$ 10³ N B)3.8 $\times$ 10⁴ N C)5.0 $\times$ 10⁴ N D)1.0 $\times$ 10⁵ N E)6.5 $\times$ 10⁴ N

Question

Quizplus · Accepted Answer

The lifting force on the roof can be calculated using the equation: 
Lifting force = Pressure difference x Area 
The pressure difference can be calculated using Bernoulli's equation: 
ΔP = ½ρv2 
where ΔP is the pressure difference, ρ is the density of air, and v is the velocity of the wind.

Substituting the given values: 
ΔP = ½ x 1.3 kg/m³ x (100 km/hr / 3.6)² = 190.3 Pa

The area of the roof is: 
Area = 10 m x 10 m = 100 m²

Therefore, the lifting force on the roof is: 
Lifting force = ΔP x Area = 190.3 Pa x 100 m² = 19030 N

Rounding off to the nearest tenth: 
Lifting force = 19000 N = 5.0 x 10³ N

Hence, option C (5.0 x 10³ N) is the best choice.

A Hurricane Strength Wind Is Blowing at a Speed of 100