5. Compared to your current weight, what would happen to your weight if BOTH the mass AND the radius of the Earth were three times greater than they are now? "My weight would be what it is now".
5. Compared to your current weight, what would happen to your weight if BOTH the mass AND the radius of the Earth were three times greater than they are now? "My weight would be what it is now".
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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Question 5
![### Gravitational Impact on Weight
In this exercise, we will explore how changes in the Earth's mass and radius would affect your weight. Your weight is the force exerted on you by gravity, which can change if either the mass of the Earth or its radius changes.
#### Question 5:
**Scenario:**
Compared to your current weight, what would happen to your weight if BOTH the mass and the radius of the Earth were three times greater than they are now?
**Statement to Complete:**
"My weight would be ______ what it is now".
**Explanation:**
In this scenario, both the mass and the radius of the Earth are increased by a factor of three. We need to apply the gravitational force formula to determine the new weight:
\[ F = G \frac{m_1 m_2}{r^2} \]
Where:
- \( F \) is the gravitational force (your weight),
- \( G \) is the gravitational constant,
- \( m_1 \) is your mass,
- \( m_2 \) is the Earth's mass,
- \( r \) is the radius of the Earth.
If \( m_2 \) becomes \( 3m_2 \) and \( r \) becomes \( 3r \):
\[ F' = G \frac{m_1 (3m_2)}{(3r)^2} = G \frac{m_1 (3m_2)}{9r^2} = \frac{1}{3} \left( G \frac{m_1 m_2}{r^2} \right) \]
Therefore, your new weight would be \(\frac{1}{3}\) of your current weight.
#### Question 6:
**Scenario:**
Compared to your current weight, what would happen to your weight if the mass of the Earth was nine times greater, while the radius of the Earth was three times greater than they are now?
**Statement to Complete:**
"My weight would be ______ what it is now".
**Explanation:**
In this scenario, the mass of the Earth increases by a factor of nine and the radius increases by a factor of three. Using the gravitational force formula:
\[ F = G \frac{m_1 m_2}{r^2} \]
If \( m_2 \) becomes \( 9m_2 \) and \( r \) becomes \( 3r \):](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0a863c3-fa8c-48bd-b04e-df2a1854546a%2F1cc3e694-85e9-42dd-9378-9aa6aa4c7097%2Ftr8c5hm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Gravitational Impact on Weight
In this exercise, we will explore how changes in the Earth's mass and radius would affect your weight. Your weight is the force exerted on you by gravity, which can change if either the mass of the Earth or its radius changes.
#### Question 5:
**Scenario:**
Compared to your current weight, what would happen to your weight if BOTH the mass and the radius of the Earth were three times greater than they are now?
**Statement to Complete:**
"My weight would be ______ what it is now".
**Explanation:**
In this scenario, both the mass and the radius of the Earth are increased by a factor of three. We need to apply the gravitational force formula to determine the new weight:
\[ F = G \frac{m_1 m_2}{r^2} \]
Where:
- \( F \) is the gravitational force (your weight),
- \( G \) is the gravitational constant,
- \( m_1 \) is your mass,
- \( m_2 \) is the Earth's mass,
- \( r \) is the radius of the Earth.
If \( m_2 \) becomes \( 3m_2 \) and \( r \) becomes \( 3r \):
\[ F' = G \frac{m_1 (3m_2)}{(3r)^2} = G \frac{m_1 (3m_2)}{9r^2} = \frac{1}{3} \left( G \frac{m_1 m_2}{r^2} \right) \]
Therefore, your new weight would be \(\frac{1}{3}\) of your current weight.
#### Question 6:
**Scenario:**
Compared to your current weight, what would happen to your weight if the mass of the Earth was nine times greater, while the radius of the Earth was three times greater than they are now?
**Statement to Complete:**
"My weight would be ______ what it is now".
**Explanation:**
In this scenario, the mass of the Earth increases by a factor of nine and the radius increases by a factor of three. Using the gravitational force formula:
\[ F = G \frac{m_1 m_2}{r^2} \]
If \( m_2 \) becomes \( 9m_2 \) and \( r \) becomes \( 3r \):
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