Question

	set 1	set 2
mass 1	700 kg	700 kg
mass 2	1,200 kg	1,200 kg
distance	11 m	11 m

which set has more gravitational force energy?
remember : $f = \frac{-g(m_1m_2)}{d^2}$
set 2
set 1
the sets have an equal amount of gravitational force energy.

Explanation:

Step1: Analyze the formula

The formula for gravitational force is \( F = \frac{-G(m_1m_2)}{d^2} \). The magnitude of the gravitational force depends on the product of the masses (\(m_1m_2\)) and the square of the distance (\(d^2\)). Since \(G\) is a constant, we can compare the forces by looking at \( \frac{m_1m_2}{d^2} \) for each set.

Step2: Calculate for Set 1

For Set 1: \(m_1 = 700\) kg, \(m_2 = 1200\) kg, \(d = 11\) m.
Calculate \(m_1m_2 = 700\times1200 = 840000\) kg².
\(d^2 = 11^2 = 121\) m².
So, \( \frac{m_1m_2}{d^2} = \frac{840000}{121} \approx 6942.15 \).

Step3: Calculate for Set 2

For Set 2: \(m_1 = 700\) kg, \(m_2 = 1200\) kg, \(d = 11\) m.
Calculate \(m_1m_2 = 700\times1200 = 840000\) kg².
\(d^2 = 11^2 = 121\) m².
So, \( \frac{m_1m_2}{d^2} = \frac{840000}{121} \approx 6942.15 \).

Step4: Compare the two sets

Since the product of the masses and the distance are the same for both sets, the value of \( \frac{m_1m_2}{d^2} \) is the same for both sets. Therefore, the magnitude of the gravitational force (ignoring the negative sign which indicates direction) is the same for both sets.

Answer:

The sets have an equal amount of gravitational force energy.