Question

	set 1	set 2
mass 1	1,500 kg	1,500 kg
mass 2	80 kg	80 kg
distance	20 m	15 m

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

Explanation:

Step1: Analyze the formula for gravitational force

The formula for gravitational force is \( F = \frac{G(m_1m_2)}{d^2} \), where \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses, and \( d \) is the distance between them. Since \( G \), \( m_1 \), and \( m_2 \) are the same for both sets, the force depends inversely on the square of the distance (\( d^2 \)).

Step2: Compare the distances of the two sets

For Set 1, \( d_1 = 20 \, \text{m} \), so \( d_1^2 = 20^2 = 400 \, \text{m}^2 \). For Set 2, \( d_2 = 15 \, \text{m} \), so \( d_2^2 = 15^2 = 225 \, \text{m}^2 \).

Step3: Relate distance squared to gravitational force

Since the force is inversely proportional to \( d^2 \), a smaller \( d^2 \) means a larger force. Since \( 225 < 400 \) (i.e., \( d_2^2 < d_1^2 \)), the gravitational force for Set 2 will be larger (because \( F \) is inversely related to \( d^2 \); when \( d^2 \) is smaller, \( F \) is larger, given the same numerator \( G(m_1m_2) \)).

Answer:

Set 2