Question

Revised question: Suppose a flat roof has a surface area of 1.39×10²m². Presume the air inside the building (and under the roof) is at atmospheric pressure, 1.01325×10⁵Pa, and that the air racing across the top of the roof is at a pressure of 1.00437×10⁵Pa. What is the force with which the air inside the house pushes the roof upward?

Answer 1

Using the principle of atmospheric pressure, the force with which the air inside the building pushes the roof upward can be calculated. The force is approximately 123.432 N.

Step-by-step explanation:

Calculating the force with which the air inside the building pushes the roof upward can be done using the principle of atmospheric pressure. We know that the atmospheric pressure at sea level is around 1.01 × 105 Pa, which equals the weight of a column of air over a 1 m² area. We can use this information to calculate the force exerted on the roof by the air inside the building if we know the difference in pressure between the air inside and outside.

The formula for calculating the force due to pressure is:

Force = Pressure × Area

Using the given values:

Pressure difference = 1.01325 × 105 Pa - 1.00437 × 105 Pa = 8.88 × 102 Pa

Area = 1.39 × 102 m²

Substituting these values into the formula:

Force = (8.88 × 102 Pa) × (1.39 × 102 m²)

Simplifying the expression:

Force = 123.432 N

Hence, the force with which the air inside the building pushes the roof upward is approximately 123.432 N.