A circular-motion addict of mass 80 kg rides a Ferris wheel...

Name: Problem 47, Chapter 6: Principles of Physics
Uploaded: 2022-03-19T12:22:52-08:00
Duration: 3 min 33 s
Channel: Sandeep Kumar Dhania
Description: A circular-motion addict of mass 80 kg rides a Ferris wheel around in a vertical circle of radius 12 m at a constant speed of 5.5 m/s. (a) What is the period of the motion? What is the magnitude of the normal force on the addict from the seat when both go through (b) the highest point of the circular path and (c) the lowest point?

A circular-motion addict of mass 80 kg rides a Ferris wheel around in a vertical circle of radius 12 m at a constant speed of 5.5 m/s. (a) What is the period of the motion? What is the magnitude of the normal force on the addict from the seat when both go through (b) the highest point of the circular path and (c) the lowest point?

A circular-motion addict of mass 80 kg rides a Ferris wheel
around in a vertical circle of radius 12 m at a constant speed of 5.5
m/s. (a) What is the period of the motion? What is the magnitude of
the normal force on the addict from the seat when both go through
(b) the highest point of the circular path and (c) the lowest point?

Key Concepts

Uniform Circular Motion

Uniform circular motion refers to the motion of an object traveling at a constant speed along a circular path. The key characteristic is that while the speed remains constant, the direction of the velocity changes continuously. This continual change in direction constitutes an acceleration directed towards the center of the circle, known as centripetal acceleration.

Period of Motion

The period of motion is the time required for an object to complete one full cycle or revolution around a circular path. It can be calculated by dividing the circumference of the circle by the constant speed of the object. This concept is fundamental in analyzing any oscillatory or circular motion.

Centripetal Force

Centripetal force is the net force required to keep an object moving in a circular path, and it acts towards the center of the circle. In the context of uniform circular motion, its magnitude is given by the product of the mass of the object and the square of its speed, divided by the radius of the circle. This force is essential for maintaining circular motion and is provided by various sources depending on the context, such as tension, gravity, or normal forces.

Normal Force

Normal force is the contact force exerted by a surface to support the weight of an object and prevent it from moving through the surface. In vertical circular motion, the normal force can vary depending on the object's position along the path. At different points in the circular trajectory, such as the highest or lowest points, the normal force adjusts to provide both support against gravitational pull and the necessary centripetal force.

Gravitational Force

Gravitational force is the force of attraction between Earth and any object near its surface, typically characterized by the product of the object's mass and the acceleration due to gravity. In problems involving vertical circular motion, this force plays a critical role by either adding to or subtracting from the net force required for centripetal acceleration, thereby influencing the magnitude of the normal force or other supporting forces.

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