Final answer:
The net force on the man at point x in the giant wheel would be the sum of the centripetal force and the gravitational force. It is assumed that the normal force is equal to the man's weight, hence the wheel must exert an equal force on the ground by Newton's third law.
Step-by-step explanation:
Understanding the Forces on the Man in a Giant Wheel
The scenario described involves a giant wheel with a diameter of 40 meters and a cage where a man of mass m stands. It is stated that the wheel rotates at a speed such that when the cage is at point x, the force exerted by the man on the platform is equal to his weight. This implies that the normal force (N) experienced by the man is equal to his weight, represented by the equation F1 = mg, where g is the acceleration due to gravity, and m denotes the mass of the man.
In a similar scenario, if a free-body diagram is used, the normal force equation is represented as Fi + N = W, leading to N = W - Fi. For instance, if a man has a mass of 45.0 kg and is experiencing a force that reduces the normal force by 32.4 N, then the normal force would be N = (45.0 kg)(9.80 m/s²) - 32.4 N = 409 N.
By Newton's third law, the force the wheel exerts on the ground would also be 409 N. The net force on the man at point x in the question would be the sum of the centripetal force needed to keep him moving in a circular path and the gravitational force (his weight).
For further understanding of multiple forces on a system, consider the case of a centrifuge or a bicyclist negotiating a turn, where the centripetal force needed for circular motion is crucial.