(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
11th Edition
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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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Need help with part C and and the bonus practice questions
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5302243e-bfe3-4faa-a729-c9f62eae2691%2F2f3bcb25-ce40-4a45-8e01-ad040f615591%2Frrdpsue_processed.png&w=3840&q=75)
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:
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
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