Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
Let's determine which set has the greater gravitational force using the provided gravitational force formula:
[tex]\[ F = \frac{-G \left(m_1 m_2\right)}{d^2} \][/tex]
where:
- \( G \) (the gravitational constant) is approximately \( 6.67430 \times 10^{-11} \) m³ kg⁻¹ s⁻².
- \( m_1 \) and \( m_2 \) are the masses in kilograms.
- \( d \) is the distance between the masses in meters.
### For Set 1:
- \( m_1 = 500 \) kg
- \( m_2 = 750 \) kg
- \( d = 3 \) meters
Plugging these values into the formula:
[tex]\[ F_{\text{Set 1}} = \frac{-G \times (500 \times 750)}{3^2} \][/tex]
This gives a gravitational force of approximately \(-2.780958333333333 \times 10^{-6}\) N.
### For Set 2:
- \( m_1 = 500 \) kg
- \( m_2 = 1000 \) kg
- \( d = 3 \) meters
Plugging these values into the formula:
[tex]\[ F_{\text{Set 2}} = \frac{-G \times (500 \times 1000)}{3^2} \][/tex]
This gives a gravitational force of approximately \(-3.707944444444444 \times 10^{-6}\) N.
### Comparing the Forces:
The gravitational force for Set 1 is \(-2.780958333333333 \times 10^{-6}\) N, and the gravitational force for Set 2 is \(-3.707944444444444 \times 10^{-6}\) N.
Since \(-3.707944444444444 \times 10^{-6}\) N (Set 2) is more negative (greater in magnitude) than \(-2.780958333333333 \times 10^{-6}\) N (Set 1), the gravitational force in Set 2 is stronger than that in Set 1.
### Conclusion:
Set 2 has more gravitational force energy.
[tex]\[ F = \frac{-G \left(m_1 m_2\right)}{d^2} \][/tex]
where:
- \( G \) (the gravitational constant) is approximately \( 6.67430 \times 10^{-11} \) m³ kg⁻¹ s⁻².
- \( m_1 \) and \( m_2 \) are the masses in kilograms.
- \( d \) is the distance between the masses in meters.
### For Set 1:
- \( m_1 = 500 \) kg
- \( m_2 = 750 \) kg
- \( d = 3 \) meters
Plugging these values into the formula:
[tex]\[ F_{\text{Set 1}} = \frac{-G \times (500 \times 750)}{3^2} \][/tex]
This gives a gravitational force of approximately \(-2.780958333333333 \times 10^{-6}\) N.
### For Set 2:
- \( m_1 = 500 \) kg
- \( m_2 = 1000 \) kg
- \( d = 3 \) meters
Plugging these values into the formula:
[tex]\[ F_{\text{Set 2}} = \frac{-G \times (500 \times 1000)}{3^2} \][/tex]
This gives a gravitational force of approximately \(-3.707944444444444 \times 10^{-6}\) N.
### Comparing the Forces:
The gravitational force for Set 1 is \(-2.780958333333333 \times 10^{-6}\) N, and the gravitational force for Set 2 is \(-3.707944444444444 \times 10^{-6}\) N.
Since \(-3.707944444444444 \times 10^{-6}\) N (Set 2) is more negative (greater in magnitude) than \(-2.780958333333333 \times 10^{-6}\) N (Set 1), the gravitational force in Set 2 is stronger than that in Set 1.
### Conclusion:
Set 2 has more gravitational force energy.
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.