Homework Help is Here – Start Your Trial Now!
Science
Physics
(c) We know that gravity, constant in magnitude g along the surface of the Earth and headed towards the centre of the Earth, is the reason why you'd stay put on the rotating sphere that is the Earth. You may notice that gravity alone does not account for the net force in (b), implying that a second force is present that maintains your motion. Draw a complete diagramme of the forces acting on you, and find this second force, both magnitude and direction. (Remember that the unit radial vector is denoted î.) BONUS: Consider the behaviour of the force you find in (c) as you change 0. Based on this behaviour, would the Earth truly be a perfect sphere? Why or why not?

(c) We know that gravity, constant in magnitude g along the surface of the Earth and headed towards the centre of the Earth, is the reason why you'd stay put on the rotating sphere that is the Earth. You may notice that gravity alone does not account for the net force in (b), implying that a second force is present that maintains your motion. Draw a complete diagramme of the forces acting on you, and find this second force, both magnitude and direction. (Remember that the unit radial vector is denoted î.) BONUS: Consider the behaviour of the force you find in (c) as you change 0. Based on this behaviour, would the Earth truly be a perfect sphere? Why or why not?

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

Need help with part C and and the bonus practice questions

## Problem 1: Understanding Forces on a Rotating Earth Let's consider the Earth as a sphere rotating at some constant angular velocity \(\vec{\omega}\) about the axis through its poles. You, of mass \(m\), are at some point on the surface of the Earth, at some angle \(\theta\) above the equator, as illustrated in the diagram below: ![Diagram of Earth illustrating the rotation axis and a point on the surface](image_link) In this diagram: - The Earth is shown as a sphere with a vertical axis representing the rotation axis. - An angular velocity \(\vec{\omega}\) is indicated, showing the direction of Earth's rotation. - A point on the Earth's surface is marked, identifying the position of an object at an angle \(\theta\) above the equator. - \(R\) represents the radius of the Earth. - The dashed lines and the angle \(\theta\) indicate the position of the object relative to the equator and the center of the Earth. ### Analysis of Forces (Part c) **(c)** We know that gravity, constant in magnitude \(g\) along the surface of the Earth and directed toward the center of the Earth, is the reason why you stay put on the rotating sphere that is the Earth. However, gravity alone does not account for the net force on you, which implies that a second force is present that maintains your motion. Draw a complete diagram of the forces acting on you and find this second force, specifying both its magnitude and direction. (Remember that the unit radial vector is denoted \(\hat{r}\).) ### Bonus Analysis **BONUS:** Consider the behavior of the force you identified in part (c) as you change \(\theta\). Based on this behavior, would the Earth truly be a perfect sphere? Why or why not? --- ### Force Diagram Explanation To solve part (c), analyze the following forces acting on the object: 1. **Gravitational Force (\(F_g\))**: This force acts towards the center of the Earth (\(-\hat{r}\) direction) with a magnitude of \(mg\). 2. **Centripetal Force (\(F_c\))**: Due to the Earth's rotation, a centripetal force is necessary to keep the object in circular motion. This force acts towards the axis of rotation. By resolving these forces into components and applying Newton's
Transcribed Image Text:## Problem 1: Understanding Forces on a Rotating Earth Let's consider the Earth as a sphere rotating at some constant angular velocity \(\vec{\omega}\) about the axis through its poles. You, of mass \(m\), are at some point on the surface of the Earth, at some angle \(\theta\) above the equator, as illustrated in the diagram below: ![Diagram of Earth illustrating the rotation axis and a point on the surface](image_link) In this diagram: - The Earth is shown as a sphere with a vertical axis representing the rotation axis. - An angular velocity \(\vec{\omega}\) is indicated, showing the direction of Earth's rotation. - A point on the Earth's surface is marked, identifying the position of an object at an angle \(\theta\) above the equator. - \(R\) represents the radius of the Earth. - The dashed lines and the angle \(\theta\) indicate the position of the object relative to the equator and the center of the Earth. ### Analysis of Forces (Part c) **(c)** We know that gravity, constant in magnitude \(g\) along the surface of the Earth and directed toward the center of the Earth, is the reason why you stay put on the rotating sphere that is the Earth. However, gravity alone does not account for the net force on you, which implies that a second force is present that maintains your motion. Draw a complete diagram of the forces acting on you and find this second force, specifying both its magnitude and direction. (Remember that the unit radial vector is denoted \(\hat{r}\).) ### Bonus Analysis **BONUS:** Consider the behavior of the force you identified in part (c) as you change \(\theta\). Based on this behavior, would the Earth truly be a perfect sphere? Why or why not? --- ### Force Diagram Explanation To solve part (c), analyze the following forces acting on the object: 1. **Gravitational Force (\(F_g\))**: This force acts towards the center of the Earth (\(-\hat{r}\) direction) with a magnitude of \(mg\). 2. **Centripetal Force (\(F_c\))**: Due to the Earth's rotation, a centripetal force is necessary to keep the object in circular motion. This force acts towards the axis of rotation. By resolving these forces into components and applying Newton's
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Space-time
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