Question

	set 1	set 2
mass 1	200 kg	200 kg
mass 2	450 kg	300 kg
distance	2 m	2 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 gravitational force formula is \( F = \frac{-G(m_1m_2)}{d^2} \). The magnitude of the force depends on \( m_1m_2 \) (since \( G \) and \( d^2 \) are the same for both sets).

Step2: Calculate \( m_1m_2 \) for Set 1

For Set 1: \( m_1 = 200 \, \text{kg} \), \( m_2 = 450 \, \text{kg} \). So \( m_1m_2 = 200 \times 450 = 90000 \, \text{kg}^2 \).

Step3: Calculate \( m_1m_2 \) for Set 2

For Set 2: \( m_1 = 200 \, \text{kg} \), \( m_2 = 300 \, \text{kg} \). So \( m_1m_2 = 200 \times 300 = 60000 \, \text{kg}^2 \).

Step4: Compare the products

Since \( 90000 > 60000 \), the magnitude of the gravitational force (ignoring the negative sign for magnitude comparison) for Set 1 is larger.

Answer:

Set 1