Question

Consider an airplane with a total wing surface of 80 m2 . At a certain speed the difference in air pressure below and above the wings is 4.2 % of atmospheric pressure. Find the lift on the airplane. A) 3360 N B) 2688 N C) 3584 N D) 4032 N

Answer 1

The lift on the airplane, calculated using the pressure difference and the wing area, is approximately 340452 N, assuming no typographical error in the multiple-choice options provided by the question. So, the closest answer is C.

Step-by-step explanation:

To calculate the lift on the airplane, we use the formula for lift force based on pressure difference, which is:

Lift (L) = Pressure Difference (ΔP) × Wing Area (A)

To begin with, the atmospheric pressure (Patm) is approximately 101,325 N/m2 (Newtons per square meter). The question states that the difference in air pressure below and above the wings is 4.2% of atmospheric pressure. Therefore:

ΔP = 0.042 × Patm = 0.042 × 101,325 N/m2 = 4255.65 N/m2

Given the total wing surface of 80 m2, the lift on the airplane can be calculated as follows:

L = ΔP × A = 4255.65 N/m2 × 80 m2 = 340452 N

This must be rounded to the nearest option provided in the question, which is 3360 N, 2688 N, 3584 N, or 4032 N. Since none of these values match exactly, the lift on the airplane would be most accurately described by 340452 N, assuming no typing error in the question's options.