How Do Aerodynamics Affect an Airplane's Lift and Drag Forces?

[emperror123]

1. an aeroplane of mass 300 tonnes during ascent travels at a constant velocity of 100 m/s. its angle of ascent is 10° to the horizontal. the trust produced by engines is 9000kN. Determine
i)the lift force acting on the wings
ii) the resistance to motion

i were trying to use f=ma, but the question didnt mention about the time, is it we need to convert 9000kN to acceleration in order to get time is second or can i get it from the question above, in other way i research via google with other website, some get F = 0N, is it possible?

secondly, the resistance is it = lift force or is it a drag force

thank

 

[Delphi51]

Welcome to PF, emperror.
The plane is not accelerating, so both the vertical and horizontal forces must be zero. For the vertical forces, you have a component of thrust upward, lift upward and the weight downward. You also have a component of the drag (resistance to motion) downward. Looks like two unknowns there, so you will have to write a similar equation for the horizontal forces and solve the two as a system.

 

[emperror123]

u mean i have to find the vertical axis 1st before i can do the horizontal axis?
and i can assume that the velocity with angle with 0N?

thrust is it on horizontal or vertical? cause u said that the thrust is upward (y-axis), make me doubt on whether is it horizontal or vertical

thank for you reply

 

[Delphi51]

Note that thrust and drag are partly horizontal and partly vertical.
You must use sine and cosine to get their horizontal and vertical components.
The vertical component of thrust will be 9000 kN *sin(10).
Recommend you start with the horizontal part; looks like it will be easy to solve for the drag.

 

[asteriatic]

you

First, it is important to clarify that force and velocity are not directly related. Force is a vector quantity that describes the interaction between two objects, while velocity is a vector quantity that describes the rate of change of an object's position. However, the force of an object can affect its velocity.

In this scenario, we can use the formula F=ma to determine the lift force acting on the wings of the airplane. The mass (m) of the airplane is given as 300 tonnes, which is equivalent to 300,000 kg. The acceleration (a) can be calculated using the velocity (v) and angle of ascent (θ) as follows:

a = v²sinθ / g

Where g is the acceleration due to gravity (9.8 m/s²). Plugging in the values, we get:

a = (100 m/s)² x sin(10°) / (9.8 m/s²) = 17.3 m/s²

Now, we can calculate the lift force (F) using the formula:

F = ma = (300,000 kg) x (17.3 m/s²) = 5,190,000 N or 5.19 MN

This is the force exerted by the wings of the airplane to keep it in constant motion.

Next, the resistance to motion is not the same as the lift force. The resistance to motion, also known as drag force, is the force that opposes the motion of the airplane and is caused by factors such as air resistance and friction. It can be calculated using the formula:

R = ½ρv²ACd

Where ρ is the density of air, v is the velocity, A is the frontal area of the airplane, and Cd is the drag coefficient. Since these values are not given in the scenario, it is not possible to calculate the exact value of the resistance to motion. However, it is safe to assume that it will be a significant force considering the large size and speed of the airplane.

In conclusion, the lift force acting on the wings of the airplane is 5.19 MN and the resistance to motion, or drag force, is a force that opposes the motion of the airplane and cannot be accurately determined without additional information.