a plane is flying with a constant speed along a straight line at an angle of 60degree with the horizontal.the weight W of the plane is 90,000N and its engine provides a thrust Tof 120,000N 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 oppposite to the direction of motion.Draw the free body diagram showing all the forces on the plane.Determine F and R.

To analyze the forces acting on the plane flying at an angle of 60 degrees with the horizontal, we can start by drawing a free body diagram. This diagram will help us visualize the forces involved and set up the equations needed to find the lift force (F) and the air resistance force (R).

Free Body Diagram Overview

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

• Weight (W): This force acts vertically downward and is equal to 90,000 N.
• Thrust (T): This force 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.
• Air Resistance (R): This force opposes the direction of motion of the plane.

Setting Up the Forces

Since the plane is flying at a constant speed, we know that the net force acting on it must be zero. This means that the forces in both the vertical and horizontal directions must balance out. Let's break down the forces into their components.

Vertical Forces

In the vertical direction, we have:

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

For vertical equilibrium, we can write the equation:

F - W = 0

Thus, we can express the lift force as:

F = W = 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

From this, we can express the air resistance as:

R = T = 120,000 N

Summary of Forces

To summarize, we have determined the following forces acting on the plane:

• Lift Force (F): 90,000 N (acting upward)
• Air Resistance (R): 120,000 N (acting backward)

This analysis shows that the plane is in equilibrium, with the lift balancing the weight and the thrust balancing the air resistance. Understanding these forces is crucial for comprehending how aircraft maintain flight and navigate through the air.