Question

A plane is flying with a constant speed along a straight line at an angle of 30

with the horizontal. The weight of the plane is 100000 N and its engine provides

a thrust of 120000 N in the direction of flight. Two additional forces are exerted

on the plane: the lift force perpendicular to the plane’s wings, and the force due

to air resistance opposite to the direction of motion. Draw the free-body diagram

showing all forces on the plane. Determine the lift force and the force due to air

resistance.​

Answer 1

The Lift force provided by wings is F = 86,600 N and the Resistance force is R = 70,000 N

Explanation:

To find:

The lift force "F" = ?

Force due to air resistance "R" = ?

Solution:

Lift force provided by the wings "F" = W cos (30°)

Lift force provided by the wings "F" = 100000 x 0.866

Lift force provided by the wings "F" = 86,600 N

T = Weight component down the slope + R

120000 = (100000 sin 30) + R

R = 120000 - 50000 = 70,000 N

Thus the Lift force provided by wings is F = 86,600 N and the Resistance force is R = 70,000 N

Answer 2

Lift force F = 86,600 N

Resistance force R = 70,000 N

Explanation:

Given: Angle = 30°

Weight of plane = 100000 N

Thrust force provided by engine = 120000 N

Find: The lift force F and force due to air resistance R.

Solution:

Lift force provided by the wings F = W cos 30°

Lift force provided by the wings F = 100000 x 0.866

Lift force provided by the wings F = 86,600 N

T = Weight component down the slope + R

120000 = (100000. sin 30°) + R

Therefore R = 120000 - 50000 = 70,000 N

Hence the Lift force provided by wings F = 86,600 N and the Resistance force R = 70,000 N