You have just read about the role of metal fatigue in airplane accidents. Metal

Question

You have just read about the role of metal fatigue in airplane accidents. Metal fatigue results from the flexing of airframe parts in response to the forces on the plane, two of which are the “lift”, an upward force on the wings perpendicular to their surface that is caused by the air, and the “drag”, a force also caused by the air that is opposite to the velocity of the plane. Calculate the size of the "drag" force for the example airplane cited in the article, which has a take-off weight of W=900000 N and take-off speed of vi=100 m/s. This plane climbs at an angle of =30° with a constant acceleration to reach its cruising altitude h= 9180 m and final speed vf=220 m/s. The engines on this plane provide a forward thrust of F=1050000 N.

Explanation / Answer

theta = 30 degree

vi = 100 m/s

vf = 220 m/s

h = 9180 m

let the acceleration is a

vf^2 - vi^2 = 2 * a * (h/sin(theta))

220^2 - 100^2 = 2 * a * (9180/sin(30))

solving for a

a = 1.046 m/s^2

let the drag force is Fd

Using second law of motion

F - Fd = m * a

1050000 - Fd = (900000/9.8) * 1.046

solving for Fd

Fd = 9533961 N

the drag force acting on the plane is 9533961 N

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