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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![### Understanding the Impact of Changes in Earth's Properties on Weight
2. **Question:**
- Compared to your current weight, what would happen to your weight if the radius of the Earth was three times greater than it is now?
- Fill in the blank: "My weight would be ______ what it is now".
3. **Question:**
- Compared to your current weight, what would happen to your weight if BOTH the radius and the mass of the Earth were three times greater than they are now?
- Fill in the blank: "My weight would be ______ what it is now".
4. **Question:**
- Compared to your current weight, what would happen to your weight if BOTH the mass of the Earth, AND YOUR mass, were three times greater than they are now?
- Fill in the blank: "My weight would be ______ what it is now".
Understanding these concepts requires knowledge of gravitational forces and how they are affected by changes in the mass and radius of the Earth.
For further insights, refer to the equations governing gravitational force:
\[ F = G \frac{m_1 m_2}{r^2} \]
where:
- \( F \) is the gravitational force between two masses,
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses,
- \( r \) is the distance between the centers of the two masses.
### Explanations:
1. **Impact of Increasing Earth's Radius by Three Times:**
- The gravitational force is inversely proportional to the square of the radius. Increasing the radius would decrease the gravitational force.
2. **Impact of Increasing Both Earth's Radius and Mass by Three Times:**
- Increasing the mass increases the gravitational pull, while increasing the radius decreases it. The net effect depends on the relative changes in mass and radius.
3. **Impact of Increasing Both Earth's Mass and Your Mass by Three Times:**
- Increasing both masses would significantly alter the gravitational force, leading to a substantial net increase in your weight.
These hypothetical scenarios allow students to explore and understand gravitational concepts in various contexts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0a863c3-fa8c-48bd-b04e-df2a1854546a%2F170784a4-98dc-4e58-822b-8906fb33148c%2Fa88z7le_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding the Impact of Changes in Earth's Properties on Weight
2. **Question:**
- Compared to your current weight, what would happen to your weight if the radius of the Earth was three times greater than it is now?
- Fill in the blank: "My weight would be ______ what it is now".
3. **Question:**
- Compared to your current weight, what would happen to your weight if BOTH the radius and the mass of the Earth were three times greater than they are now?
- Fill in the blank: "My weight would be ______ what it is now".
4. **Question:**
- Compared to your current weight, what would happen to your weight if BOTH the mass of the Earth, AND YOUR mass, were three times greater than they are now?
- Fill in the blank: "My weight would be ______ what it is now".
Understanding these concepts requires knowledge of gravitational forces and how they are affected by changes in the mass and radius of the Earth.
For further insights, refer to the equations governing gravitational force:
\[ F = G \frac{m_1 m_2}{r^2} \]
where:
- \( F \) is the gravitational force between two masses,
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses,
- \( r \) is the distance between the centers of the two masses.
### Explanations:
1. **Impact of Increasing Earth's Radius by Three Times:**
- The gravitational force is inversely proportional to the square of the radius. Increasing the radius would decrease the gravitational force.
2. **Impact of Increasing Both Earth's Radius and Mass by Three Times:**
- Increasing the mass increases the gravitational pull, while increasing the radius decreases it. The net effect depends on the relative changes in mass and radius.
3. **Impact of Increasing Both Earth's Mass and Your Mass by Three Times:**
- Increasing both masses would significantly alter the gravitational force, leading to a substantial net increase in your weight.
These hypothetical scenarios allow students to explore and understand gravitational concepts in various contexts.
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