Homework Help is Here – Start Your Trial Now!
Science
Physics
A uniform solid sphere of radius R = 0.200 m and mass M = 1.85 kg starts from a height vertical H on an inclined plane and rolls DOWN the incline without slipping. The initial translational speed of the center of mass of the sphere is ZERO. Thus, the solid sphere begins from REST. Assume H= 20.0 m, about 66 feet. Use the rotational inertia I for a solid sphere. (PLEASE FIGURE 10. 21 IN THE E-BOOK OR ICQ16 for the rotational inertia of a sphere) I = (2/5) * MR². Show all work. If you do not consider the rotational part of the kinetic energy, you will get a zero on this problem. (a) 2 What is the final translational speed V₂ of the center of mass of the sphere at the bottom? (b) What is the final angular speed | o₂ | about the center of mass of the sphere at the bottom? IN OTHER WORDS, FIND THE MAGNITUDE OF THE ANGULAR VELOCITY AT THE BOTTOM. (c) problem? Explain. Did you need the mass M or the angle shown to solve this W₁=0 Las W₂ H 30° != ?

A uniform solid sphere of radius R = 0.200 m and mass M = 1.85 kg starts from a height vertical H on an inclined plane and rolls DOWN the incline without slipping. The initial translational speed of the center of mass of the sphere is ZERO. Thus, the solid sphere begins from REST. Assume H= 20.0 m, about 66 feet. Use the rotational inertia I for a solid sphere. (PLEASE FIGURE 10. 21 IN THE E-BOOK OR ICQ16 for the rotational inertia of a sphere) I = (2/5) * MR². Show all work. If you do not consider the rotational part of the kinetic energy, you will get a zero on this problem. (a) 2 What is the final translational speed V₂ of the center of mass of the sphere at the bottom? (b) What is the final angular speed | o₂ | about the center of mass of the sphere at the bottom? IN OTHER WORDS, FIND THE MAGNITUDE OF THE ANGULAR VELOCITY AT THE BOTTOM. (c) problem? Explain. Did you need the mass M or the angle shown to solve this W₁=0 Las W₂ H 30° != ?

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)...
See similar textbooks
icon
Related questions
Question
Please please answer everything super fast
**Title: Dynamics of a Rolling Sphere on an Incline** **Introduction:** A uniform solid sphere with radius \( R = 0.200 \, \text{m} \) and mass \( M = 1.85 \, \text{kg} \) starts rolling from rest from a vertical height \( H \) on an inclined plane. The sphere rolls down the incline without slipping. Initially, the translational speed of the sphere's center of mass is zero. **Problem Statement:** The sphere, starting from rest at a height of \( H = 20.0 \, \text{m} \) (approximately 66 feet), rolls down an incline. Use the rotational inertia \( I \) for a solid sphere, which is given by \( I = \frac{2}{5}MR^2 \). **Questions:** (a) What is the final translational speed \( V_2 \) of the center of mass of the sphere at the bottom of the incline? (b) What is the final angular speed \( |\omega_2| \) about the center of mass of the sphere at the bottom? In other words, find the magnitude of the angular velocity at the bottom. (c) Did you need the mass \( M \) or the angle shown in the diagram to solve this problem? Explain. **Diagram Explanation:** The diagram illustrates a sphere at the top of a 30-degree inclined plane with an initial angular velocity \( \omega_1 = 0 \). The sphere rolls down, reaching the bottom with a translational speed \( V_2 \) and an angular velocity \( \omega_2 \). **Note:** Failure to consider the rotational part of the kinetic energy will result in incorrect calculations. **Conclusion:** The exercise requires calculating the final translational and angular speeds using principles of rotational dynamics and conservation of energy. Understand the roles of mass, radius, and height in determining these speeds, considering the contribution of both translational and rotational motion.
Transcribed Image Text:**Title: Dynamics of a Rolling Sphere on an Incline** **Introduction:** A uniform solid sphere with radius \( R = 0.200 \, \text{m} \) and mass \( M = 1.85 \, \text{kg} \) starts rolling from rest from a vertical height \( H \) on an inclined plane. The sphere rolls down the incline without slipping. Initially, the translational speed of the sphere's center of mass is zero. **Problem Statement:** The sphere, starting from rest at a height of \( H = 20.0 \, \text{m} \) (approximately 66 feet), rolls down an incline. Use the rotational inertia \( I \) for a solid sphere, which is given by \( I = \frac{2}{5}MR^2 \). **Questions:** (a) What is the final translational speed \( V_2 \) of the center of mass of the sphere at the bottom of the incline? (b) What is the final angular speed \( |\omega_2| \) about the center of mass of the sphere at the bottom? In other words, find the magnitude of the angular velocity at the bottom. (c) Did you need the mass \( M \) or the angle shown in the diagram to solve this problem? Explain. **Diagram Explanation:** The diagram illustrates a sphere at the top of a 30-degree inclined plane with an initial angular velocity \( \omega_1 = 0 \). The sphere rolls down, reaching the bottom with a translational speed \( V_2 \) and an angular velocity \( \omega_2 \). **Note:** Failure to consider the rotational part of the kinetic energy will result in incorrect calculations. **Conclusion:** The exercise requires calculating the final translational and angular speeds using principles of rotational dynamics and conservation of energy. Understand the roles of mass, radius, and height in determining these speeds, considering the contribution of both translational and rotational motion.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Rotational Kinetic energy
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON
SEE MORE TEXTBOOKS