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\begin{tabular}{|c|c|c|}
\hline
& Set 1 & Set 2 \\
\hline
Mass 1 & [tex]$500 \, \text{kg}$[/tex] & [tex]$500 \, \text{kg}$[/tex] \\
\hline
Mass 2 & [tex]$750 \, \text{kg}$[/tex] & [tex]$1{,}000 \, \text{kg}$[/tex] \\
\hline
Distance & [tex]$3 \, \text{m}$[/tex] & [tex]$3 \, \text{m}$[/tex] \\
\hline
\end{tabular}

Which set has more gravitational force energy? Remember: [tex]$F=\frac{-G(m_1 m_2)}{d^2}$[/tex]

A. Set 1

B. Set 2

C. The sets have an equal amount of gravitational force energy.



Answer :

GinnyAnswer
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.

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