Question

	set 1	set 2
mass 1	400 kg	400 kg
mass 2	375 kg	375 kg
distance	9 m	11 m

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

Explanation:

Step1: Analyze the formula for gravitational force

The formula for gravitational force is \( F = \frac{-G(m_1m_2)}{d^2} \). Since \( G \), \( m_1 \), and \( m_2 \) are the same for both sets ( \( m_1 = 400\space kg \), \( m_2 = 375\space kg \), and \( G \) is a constant), the magnitude of the force depends on \( \frac{m_1m_2}{d^2} \). A larger value of \( \frac{m_1m_2}{d^2} \) (ignoring the negative sign which indicates direction) means a larger magnitude of gravitational force.

Step2: Calculate \( \frac{m_1m_2}{d^2} \) for Set 1

For Set 1: \( m_1 = 400\space kg \), \( m_2 = 375\space kg \), \( d = 9\space m \)
First, calculate \( m_1m_2 = 400\times375 = 150000 \)
Then, calculate \( d^2 = 9^2 = 81 \)
So, \( \frac{m_1m_2}{d^2} = \frac{150000}{81} \approx 1851.85 \)

Step3: Calculate \( \frac{m_1m_2}{d^2} \) for Set 2

For Set 2: \( m_1 = 400\space kg \), \( m_2 = 375\space kg \), \( d = 11\space m \)
First, \( m_1m_2 = 400\times375 = 150000 \) (same as Set 1)
Then, \( d^2 = 11^2 = 121 \)
So, \( \frac{m_1m_2}{d^2} = \frac{150000}{121} \approx 1239.67 \)

Step4: Compare the two values

Since \( 1851.85 > 1239.67 \), the value of \( \frac{m_1m_2}{d^2} \) for Set 1 is larger. Therefore, the magnitude of the gravitational force for Set 1 is larger (ignoring the negative sign).

Answer:

Set 1