Question

The wind in Toledo gusts up to a sustained speed of 20 m/s. Assuming the air density of 1.29 kg/m^3, calculate the total force exerted on a flat roof having an area of 100 m^2.

a) 258 N
b) 516 N
c) 2580 N
d) 5160 N

Answer 1

To calculate the total force exerted on the flat roof, use the formula Force = Pressure × Area. Given the air density and wind speed, calculate the pressure and then calculate the total force.

Step-by-step explanation:

To calculate the total force exerted on the flat roof, we can use the formula:

Force = Pressure × Area

First, we need to calculate the pressure. The pressure is given by the formula:

Pressure = 1/2 × air density × wind speed squared

Given that the air density is 1.29 kg/m³ and the wind speed is 20 m/s, we can calculate the pressure:

Pressure = 1/2 × 1.29 kg/m³ × (20 m/s)^2 = 516 N/m²

Now we can calculate the total force:

Force = 516 N/m² × 100 m² = 51600 N

The total force exerted on the flat roof is 5160 N.