Question

A plane is flying with a constant speed along a straight line at an angle of 60° with the
horizontal. The weight W of the plane is 90, 000 N and its engine provides a thrust T of
120, 000 N in the direction of flight. Two additional forces are exerted on the plane: the lift
force F perpendicular to the plane’s wings, and the force R due to air resistance opposite to
the direction of motion. Draw the free-body diagram showing all forces on the plane.
Determine F and R.

Answer 1

A plane is flying with a constant speed along a straight line at an angle of $60{}^{\circ}$ with the horizontal. The weight W of the plane is 90,000 N and its engine provides a thrust T of 120,000 N in the direction of flight. Two additional forces are exerted on the plane: the lift force F perpendicular to the plane's wings, and the force R due to air resistance opposite to the direction of motion. Draw the free-body diagram showing all forces on the plane. Determine F and R.

2-nd Newton's law in two projections:

1. F-axis

$$F - W \cos (6 0) = 0$$ $$F = W \cos (6 0)$$ $$F = 9 0 0 0 0 N * \cos (6 0) = 4 5 0 0 0 N$$

2. R-axis

$$R - T + W \cos (3 0) = 0$$ $$R = T - W \cos (3 0)$$ $$R = 1 2 0 0 0 0 N - 9 0 0 0 0 N * \cos (3 0) = 4 2 0 5 7. 7 N$$

Answer: $F = 45000N$ , $R = 42057.7N$