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

$\alpha = 30$

$mg = 80,000H$

$F_{th} = \text{of } 100,000 \mathrm{~N}$ - force of thrust

$F_{r}$ force of air resistance

$F_{l}$ - the lift force

From Newton's first law of motion:

If there is no net force on an object, then its velocity is constant.

So, vector sum of forces equals 0.

Therefore:

$F_{r} + mg\sin \alpha = F_{th}\Rightarrow F_{r} = F_{th} - mg\sin \alpha$

and:

$mg\cos \alpha = F_{l}\Rightarrow F_{l} = mg\cos \alpha = \frac{\sqrt{3}}{2} 80,000H = 69,282H$

$F_{r} = 100,000\mathrm{N} - \frac{1}{2} 80,000H = 60,000H$

Answer: the lift force equals 69,282 H and the force due to air resistance equals 60,000 H