An airplane has an effective wing surface area of 17 m2 that is generating the lift force. In level flight the air speed over the top of the wings is 63.9 m/s, while the air speed beneath the wings is 58.0 m/s. What is the weight of the plane?
Answer in N
Weight = Lift
= Area*(PressureBottom - PressureTop)
= (1/2)(air density)*Area*(V2^1 - V1^2)
V2 = 63.9 m/s
V1 = 58 m/s
Look up the air density
To find the weight of the plane, we need to use the lift equation, which relates the lift force generated by the wings to the weight of the plane.
The lift force (L) is equal to the coefficient of lift (Cl) multiplied by the air density (ρ), the wing surface area (A), and the square of the airspeed (V).
The equation can be written as:
L = Cl * ρ * A * V^2
In this case, we are given the effective wing surface area (A) as 17 m², the airspeed over the top of the wings (V₁) as 63.9 m/s, and the airspeed beneath the wings (V₂) as 58.0 m/s.
Since the lift equation requires the square of the airspeed, we need to find the average airspeed (V_avg).
V_avg = (V₁ + V₂) / 2
V_avg = (63.9 + 58.0) / 2 = 60.95 m/s
Now we can substitute the given values into the lift equation to find the lift force (L):
L = Cl * ρ * A * V_avg^2
To solve for the weight of the plane (W), we equate the lift force to the weight:
W = L
Now we need the value of the coefficient of lift (Cl), which depends on the aerodynamic characteristics of the particular aircraft. Without this information, we can't determine the exact weight of the plane.
Please provide the coefficient of lift (Cl) to continue with the calculation.