Question

set 1 set 2 mass 1 5,000 kg 4,200 kg mass 2 2,500 kg 2,500 kg distance 35 m 35 m which set has more gravitational force energy? remember : $f = \frac{-g(m_1m_2)}{d^2}$ the sets have an equal amount of gravitational force energy. set 2 set 1

Explanation:

Step1: Analyze the formula

The formula for gravitational force is \( F = \frac{-G(m_1m_2)}{d^2} \). Here, \( G \) is a constant, \( d \) is the distance (same for both sets), and the force's magnitude depends on \( m_1m_2 \) (since \( G \) and \( d^2 \) are constant for both sets). The negative sign indicates direction, not magnitude for comparison of force energy (we can consider the magnitude here as we compare which is more).

Step2: Calculate \( m_1m_2 \) for Set 1

For Set 1: \( m_1 = 5000 \, \text{kg} \), \( m_2 = 2500 \, \text{kg} \)
\( m_1m_2 = 5000 \times 2500 = 12500000 \, \text{kg}^2 \)

Step3: Calculate \( m_1m_2 \) for Set 2

For Set 2: \( m_1 = 4200 \, \text{kg} \), \( m_2 = 2500 \, \text{kg} \)
\( m_1m_2 = 4200 \times 2500 = 10500000 \, \text{kg}^2 \)

Step4: Compare the products

Since \( 12500000 > 10500000 \), the magnitude of \( \frac{G(m_1m_2)}{d^2} \) (ignoring the negative sign for magnitude comparison) is larger for Set 1. So Set 1 has more gravitational force energy.

Answer:

Set 1