An airplane has an effective wing surface area of 16 square meter that is generating the lifting force. In level flight the air speed over the top of the wings is 62m/s, while the air speed beneath the wings is 54m/s. What is the weight of the plane?
Weight = Lift
= Area*(PressureBottom - PressureTop)
= (1/2)(air density)*Area*(V2^1 - V1^2)
V2 = 62 m/s
V1 = 54 m/s
The air density depends temperature and altitude. It should be about 1.2 kg/m^3. You decide what to assume.
To find the weight of the plane, we need to first calculate the lift force acting on the wings.
The lift force can be calculated using the formula:
Lift Force = (Coefficient of Lift) x (Dynamic Pressure) x (Wing Area)
The coefficient of lift can be assumed to be 1 for level flight.
The dynamic pressure can be calculated using the formula:
Dynamic Pressure = 0.5 x (Air Density) x (Velocity^2)
Where the air density can be assumed to be 1.2 kg/m^3.
Let's calculate the dynamic pressure first:
Dynamic Pressure = 0.5 x (1.2 kg/m^3) x (62^2 m/s) = 2316.8 N/m^2
Now, let's calculate the lift force:
Lift Force = (1) x (2316.8 N/m^2) x (16 m^2) = 37148.8 N
Finally, the weight of the plane is equal to the lift force, since the plane is in level flight:
Weight of the plane = 37148.8 N
Therefore, the weight of the plane is approximately 37148.8 Newtons.
To find the weight of the plane, we need to use the concept of lift and the equation for lift force. The lift force is the upward force generated by the airplane's wings that counteracts the weight of the plane.
The equation for lift force is given by:
Lift = (Coefficient of Lift) x (0.5) x (air density) x (velocity^2) x (wing surface area)
We are given the wing surface area (16 square meters), the air speeds over and beneath the wings (62 m/s and 54 m/s respectively), but we need additional information to calculate the lift coefficient and air density.
The coefficient of lift depends on the shape of the wing (airfoil) and the angle of attack, which is the angle between the wing's chord line and the incoming airflow. The air density depends on altitude and temperature.
If you have this additional information, please provide it so I can assist you further in calculating the weight of the plane.