To determine which set has more gravitational force energy, we need to calculate the gravitational force for each set using the given formula:
[tex]\[ F = \frac{-G \left(m_1 m_2\right)}{d^2} \][/tex]
First, let's list the known values for both sets:
For Set 1:
- \( m_1 = 4300 \, \text{kg} \)
- \( m_2 = 6000 \, \text{kg} \)
- \( d = 40 \, \text{m} \)
For Set 2:
- \( m_1 = 4300 \, \text{kg} \)
- \( m_2 = 6000 \, \text{kg} \)
- \( d = 40 \, \text{m} \)
Given that the gravitational constant \( G \) is the same for both sets, and that the masses and distances are identical in both sets, we can infer that the gravitational forces will be computed from identical values.
Now, since the equation for the gravitational force depends only on the masses and the distance between them, we need to plug these values into the formula to determine the force for each set. Despite the detailed calculations being unnecessary because of the identical values, it’s clear that:
[tex]\[ F_{\text{Set 1}} = \frac{-G \left(4300 \times 6000\right)}{40^2} \][/tex]
[tex]\[ F_{\text{Set 2}} = \frac{-G \left(4300 \times 6000\right)}{40^2} \][/tex]
Since both \( F_{\text{Set 1}} \) and \( F_{\text{Set 2}} \) have identical expressions, we can conclude:
[tex]\[ F_{\text{Set 1}} = F_{\text{Set 2}} \][/tex]
Therefore, the correct answer is:
- The sets have an equal amount of gravitational force energy.
