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 80, 000 N and its engine provides a thrust of 100, 000 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

A plane is flying with a constant speed along a straight line at an angle of $30{}^{\circ}$ with the horizontal. The weight of the plane is 80,000 N and its engine provides a thrust of 100,000 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.

Solution

$F$ - lift force, $R$ - the force due to air resistance, $T$ - force provided by engine.

The lift force $F$ provided by the wings

$$F = W \cos 30 = 80,000 * \cos 30 = 69,282N.$$

As the plane has a constant speed the net force acting along the line of flight must be zero. Which means

$T =$ weight component 'down the slope' $+ R$

$$100,000 = (80,000 \cdot \sin 30) + R \rightarrow R = 100,000 - 40,000 = 60,000N$$

Answer: 69,282N; 60,000N.