Two people are separated by a distance of 0.6 m and experience a force of 1.2 x 10^-15 N. What is the force between them if the distance is doubled?

Steps to Solve

1. Identify the formula We start with the formula for the force between two objects, which follows an inverse square relationship. For gravitational force, it's given by $$ F = \frac{G \cdot m_1 \cdot m_2}{r^2} $$ where $F$ is the force, $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the objects, and $r$ is the distance between their centers.

2. Set the initial force and distance Let’s denote the initial force as $F_1$ and the initial distance as $r_1$. We will also denote the new distance (when it is doubled) as $r_2 = 2r_1$.

3. Substituting into the formula for the new force The new force $F_2$ when the distance is doubled can be expressed as: $$ F_2 = \frac{G \cdot m_1 \cdot m_2}{(2r_1)^2} $$ This simplifies to: $$ F_2 = \frac{G \cdot m_1 \cdot m_2}{4r_1^2} = \frac{1}{4} \cdot \frac{G \cdot m_1 \cdot m_2}{r_1^2} $$

4. Relating new force to initial force Since we know that $$ F_1 = \frac{G \cdot m_1 \cdot m_2}{r_1^2} $$ we can substitute $F_1$ into our expression for $F_2$: $$ F_2 = \frac{1}{4} F_1 $$

5. Final conclusion about force change This equation shows that when the distance between the two people is doubled, the force between them becomes one quarter of the initial force.