A large building shaped like a box is 60 m high with a face that is 75 m wide. A strong wind blows directly at the face of the building, exerting a pressure of 160 Upper N divided by m squared at the ground and increasing with height according to P (y) equals160plus 2y, where y is the height above the ground. Calculate the total force on the building, which is a measure of the resistance that must be included in the design of the building.

Question

Physics

Conor Lyons

16 May, 02:20

A large building shaped like a box is 60 m high with a face that is 75 m wide. A strong wind blows directly at the face of the building, exerting a pressure of 160 Upper N divided by m squared at the ground and increasing with height according to P (y) equals160plus 2y, where y is the height above the ground. Calculate the total force on the building, which is a measure of the resistance that must be included in the design of the building.

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Josh Maxwell · Answer 1

The total force on the building, which is a measure of the resistance that must be included in the design of the building is 990 KN

Explanation:

Total force = total pressure * Area of that face of the building

Taking an elemental part of the wall

Force on that part, dF = Pressure of that part * Area on that part = (160 + 2y) (75dy)

dF = 12000 dy + 150y dy

dF = (12000 + 150y) dy

Integrating both sides

∫dF = ∫ (12000 + 150y) dy

Integrating the left hand side from 0 to F and the right hand side from 0 to 60 m

F = 12000y + 75y² = 12000 (60) + 75 (60²) = 990000 N = 990 KN.