Question

Suppose a flat roof has a surface area of 8.80000×101 m². Presume the air inside the building (and under the roof) is at atmospheric pressure, 1.01325×105 Pa, and that the air racing across the top of the roof is at a pressure of 9.94857×104 Pa. What is the force with which the air inside the house pushes the roof upward?

Answer 1

The force with which the air inside the house pushes the roof upward is calculated using the formula F = P × A, where P is the atmospheric pressure inside the building (1.01325 × 105 Pa) and A is the area of the roof (8.8 × 101 m²). The resulting upward force is 8.9166 × 106 Newtons.

Step-by-step explanation:

The student asked: What is the force with which the air inside the house pushes the roof upward?

To find the force exerted by the air pressure inside the building on the roof, we use the equation F = P × A. The atmospheric pressure inside the building is 1.01325 × 105 Pa, and the area of the roof is 8.8 × 101 m². So the force exerted upwards by the internal air pressure is:

F = (1.01325 × 105 Pa) × (8.8 × 101 m²)

Calculating the values:

F = 8.9166 × 106 N

This means the upward force on the roof due to internal air pressure is 8.9166 × 106 Newtons.