5 A student of weight 667 N rides a steadily rotating Ferris...

5 A student of weight 667 N rides a steadily rotating Ferris wheel (the student sits upright). At the highest point, the magnitude of the normal force on the student from the seat is 556 N. (a) Does the student feel “light” or “heavy” there? (b) What is the magnitude of at the lowest point? If the wheel’s speed is doubled, what is the magnitude FN at the (c) highest and (d) lowest point?

5 A student of weight 667 N rides a steadily rotating Ferris
wheel (the student sits upright). At the highest point, the magnitude of the normal force on the student from the seat is 556 N.
(a) Does the student feel “light” or “heavy” there? (b) What is the
magnitude of at the lowest point? If the wheel’s speed is doubled, what is the magnitude FN at the (c) highest and (d) lowest
point?

Key Concepts

Centripetal Force

Centripetal force is the net force required to keep an object moving in a circular path, always directed toward the center of the circle. In problems involving circular motion, this force is provided by other forces acting on the object, such as the normal force or gravity, and its magnitude is dependent on the mass, velocity, and radius of the circle. This concept is critical in understanding motion on rides like Ferris wheels, where the necessary inward force changes with speed.

Normal Force in Circular Motion

The normal force is the reaction force that a surface exerts perpendicular to the contacting object. In circular motion, its magnitude can vary at different points along the path because it contributes, along with gravitational force, to providing the centripetal force. At the top of a circular path, the normal force is generally less because gravity also acts in the same direction as the required centripetal force, while at the bottom, the normal force is greater as it must overcome gravity in addition to providing centripetal acceleration.

Gravitational Force

Gravitational force is the attractive force exerted by the Earth on objects, commonly measured in newtons by the weight of the object. It plays a crucial role in circular motion scenarios, especially when analyzing forces on a Ferris wheel, as the balance between gravitational and normal forces determines the net force available for centripetal acceleration at various points along the ride.

Dependence of Centripetal Force on Speed

The required centripetal force for circular motion is proportional to the square of the speed of the moving object. This relationship means that doubling the speed will quadruple the necessary centripetal force, profoundly affecting the normal force experienced by a rider. Understanding this dependency is vital when evaluating dynamic effects such as the sensation of being lighter or heavier at different points on a Ferris wheel.

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