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A hollow ball m = 20.0 g and radius r = 1.00 cm is placed on a ramp at height H. Assuming that it rolls without slipping and referring to the image below. If R = 10.0 cm and H = 59.0 cm, does the ball stay in contact with the top of the loop? Please show your work.

A hollow ball m = 20.0 g and radius r = 1.00 cm is placed on a ramp at height H. Assuming that it rolls without slipping and referring to the image below. If R = 10.0 cm and H = 59.0 cm, does the ball stay in contact with the top of the loop? Please show your work.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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A hollow ball m = 20.0 g and radius r = 1.00 cm is placed on a ramp at height H. Assuming that it rolls without slipping and referring to the image below. If R = 10.0 cm and H = 59.0 cm, does the ball stay in contact with the top of the loop? Please show your work.

The image depicts a classic physics scenario involving a pendulum motion interacting with a circular loop. Here is a detailed explanation: 1. **Pendulum Setup:** - A small ball is at the top of a curve at a height labeled as \( H \). This represents the initial potential energy in the system which will convert into kinetic energy as the ball moves downward. 2. **Circular Loop:** - At the bottom center, there is a circular loop with a radius marked as \( R \). The ball is assumed to traverse this loop as it descends. 3. **Post-Loop Trajectory:** - The ball, having completed the loop, ascends on the other side of the track to a lower height marked as \( h \). This height indicates the remaining potential energy after some energy has been lost (perhaps through friction or air resistance). 4. **Key Labels:** - \( H \): The initial height, indicating the starting potential energy. - \( R \): The radius of the circular loop, which affects the speed needed to navigate it. - \( h \): The final height achieved after the loop, representing the remaining energy after losses. This diagram is used to illustrate concepts such as energy conservation, transformation between potential and kinetic energy, and the dynamics of circular motion.
Transcribed Image Text:The image depicts a classic physics scenario involving a pendulum motion interacting with a circular loop. Here is a detailed explanation: 1. **Pendulum Setup:** - A small ball is at the top of a curve at a height labeled as \( H \). This represents the initial potential energy in the system which will convert into kinetic energy as the ball moves downward. 2. **Circular Loop:** - At the bottom center, there is a circular loop with a radius marked as \( R \). The ball is assumed to traverse this loop as it descends. 3. **Post-Loop Trajectory:** - The ball, having completed the loop, ascends on the other side of the track to a lower height marked as \( h \). This height indicates the remaining potential energy after some energy has been lost (perhaps through friction or air resistance). 4. **Key Labels:** - \( H \): The initial height, indicating the starting potential energy. - \( R \): The radius of the circular loop, which affects the speed needed to navigate it. - \( h \): The final height achieved after the loop, representing the remaining energy after losses. This diagram is used to illustrate concepts such as energy conservation, transformation between potential and kinetic energy, and the dynamics of circular motion.
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