Final answer:
To find the lift force the wings need to generate to keep a plane moving in a circle at 126 m/s, one must calculate the centripetal acceleration and multiply it by the plane's mass. This calculation requires knowing the radius of the circular path.
Step-by-step explanation:
The question pertains to the concept of circular motion and the lift force required by an airplane's wings to maintain its motion in a circle. Specifically, if a plane is moving at 126 m/s at the bottom of a circular path, it's essential to assess the required lift from the wings to sustain this circular motion.
Lift is a force that acts perpendicular to the direction of motion and is essential for an airplane to maintain flight. According to Newton's second law (F = m * a), to find the needed lift force, we must first determine the centripetal acceleration that keeps the plane moving in a circular path. The formula for centripetal acceleration is a = v^2 / r, where v is the velocity and r is the radius of the circle.
Once the centripetal acceleration is known, we multiply it by the mass of the airplane to find the net centripetal force required. This force is essentially the lift that the wings need to generate since it acts in the upward direction, opposing the weight of the airplane, which acts downward. Hence, if the mass of the plane and the radius of the circular path are known, the calculation of the lift can be completed.