Question

a plane traveling at a speed of 180 ms⁻¹ along a horizontal circle makes an angle of 35 degrees to the horizontal. the lift face l is acting in the normal to the planes wings. calculate the radius of the circle.

Answer 1

The radius of the circle in which a plane is flying can be found by analyzing the lift force acting on the plane and its components due to the banking angle. This involves physics concepts of circular motion and forces.

Step-by-step explanation:

The question involves determining the radius of a circle in which a plane is flying horizontally while banking at an angle. The plane travels at a constant speed and maintains a banking angle to the horizontal. Using physical principles of circular motion and the concept of lift force, which acts perpendicular to the wings of the plane, the radius of the circle can be calculated.

Step-by-Step Solution:

1. Identify the forces acting on the airplane: the lift force (L) acting perpendicular to the wings, and the weight of the plane acting downwards.
2. Understand that when a plane banks at an angle, the lift force can be resolved into horizontal and vertical components. The vertical component of lift opposes the weight of the plane, and the horizontal component provides the centripetal force required for circular motion.
3. Using the banking angle (θ), the speed of the plane (v), and the acceleration due to gravity (g), the lift force can be used to find the radius (r) of the circle.

Therefore, the calculation involves finding the components of the lift force based on the angle of banking and using the horizontal component to equate it to the centripetal force, which is mass times the centripetal acceleration (mv²/r). From this, we can solve for the radius r.