A plane is flying with a constant speed along a straight line at an angle of 60 degrees 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.

To analyze the forces acting on the plane, we first need to visualize the situation with a free-body diagram. This diagram will help us identify and represent all the forces acting on the plane as it flies at an angle of 60 degrees to the horizontal. Let's break down the problem step by step.

Free-Body Diagram Overview

In the free-body diagram, we will represent the following forces:

• Weight (W): This force acts downward due to gravity, with a magnitude of 90,000 N.
• Thrust (T): The engine's thrust acts in the direction of flight, with a magnitude of 120,000 N.
• Lift (F): This force acts perpendicular to the wings of the plane, helping to keep it in the air.
• Air Resistance (R): This force opposes the direction of motion of the plane.

Setting Up the Forces

To find the lift force (F) and the air resistance (R), we can use the principles of equilibrium. Since the plane is flying at a constant speed, the net force in both the vertical and horizontal directions must equal zero.

Vertical Forces

In the vertical direction, we have:

• The weight (W) acting downward: 90,000 N
• The lift force (F) acting upward

For vertical equilibrium, we can write the equation:

F - W = 0

Substituting the weight:

F - 90,000 N = 0

This gives us:

F = 90,000 N

Horizontal Forces

In the horizontal direction, we have:

• The thrust (T) acting forward: 120,000 N
• The air resistance (R) acting backward

For horizontal equilibrium, we can write the equation:

T - R = 0

Substituting the thrust:

120,000 N - R = 0

This leads us to:

R = 120,000 N

Summary of Forces

To summarize our findings:

• The lift force (F) acting perpendicular to the wings of the plane is 90,000 N.
• The air resistance (R) opposing the motion of the plane is 120,000 N.

By understanding the balance of forces acting on the plane, we can see how it maintains its flight path despite the various forces at play. This analysis is crucial in aviation and helps engineers design safer and more efficient aircraft.