a plane is flying with a constant speed along a straight line at an angle 60degree with the horizontal. the weight(W) of the plane is 90,000N and its engine provides a thrust(T)of 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 opposite to the direction of motion . draw the free body diagram showing all the forces on the plane. determine F and R

Question

a plane is flying with a constant speed along a straight line at an angle 60degree with the horizontal. the weight(W) of the plane is 90,000N and its engine provides a thrust(T)of 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 opposite to the direction of motion . draw the free body diagram showing all the forces on the plane. determine F and R

Answer 1

To draw the free body diagram of the plane and determine the lift force and the force due to air resistance, follow these steps:

Step 1: Draw a horizontal line to represent the ground.

Step 2: Draw a vertical line perpendicular to the ground line to represent the vertical direction.

Step 3: At the origin (intersection of the ground and vertical lines), draw a line representing the direction of flight at a 60-degree angle with the horizontal line.

Step 4: Place an arrowhead on the flight direction line to indicate the direction of flight.

Now, we'll add the forces to the free body diagram:

Step 5: Label the weight force (W) downward vertically from the origin.

Step 6: Label the thrust force (T) in the direction of flight.

Step 7: Label the lift force (F) perpendicular to the plane's wings. It should be drawn as an upward force from the origin, perpendicular to the flight direction line.

Step 8: Label the force due to air resistance (R) opposite to the direction of motion. It should be drawn as a force opposing the thrust force (T) from the origin, in the opposite direction of flight.

Now, let's determine the lift force (F) and the force due to air resistance (R) using the given information:

Since the plane is flying at a constant speed, we know that the net force in the horizontal direction is zero. Therefore, the thrust force (T) and the force due to air resistance (R) are balanced.

Given:
Weight (W) = 90,000 N
Thrust (T) = 120,000 N

Since the angle between the direction of flight and the horizontal is 60 degrees, the lift force (F) can be determined by resolving the weight force (W) into two components:

Step 9: Draw a line representing the weight force (W) downward from the origin.

Step 10: Next, draw a line parallel to the flight direction line (60-degree angle line) originating from the endpoint of the weight force (W).

Step 11: Draw a line perpendicular to the flight direction line originating from the same endpoint.

Step 12: Connect the endpoints of the lines drawn in steps 10 and 11.

The resolved component of the weight force (W) in the direction perpendicular to the flight direction line represents the lift force (F). Measure the magnitude of the lift force (F) using a ruler.

To determine the force due to air resistance (R), we know that the net force in the vertical direction is zero since the plane is flying at a constant altitude.

Therefore, the weight force (W) and the lift force (F) must be balanced by an equal and opposite force due to air resistance (R).

To find the magnitude of the force due to air resistance (R), measure the length of the line representing the force due to air resistance (R) using a ruler.

You have now drawn the free body diagram and determined the magnitudes of the lift force (F) and the force due to air resistance (R).