The gravitational force between Sally and the dog is approximately \(1.00 \times 10^{-6} \, \text{N}\).
The gravitational force (\(F\)) between two objects is given by Newton's law of gravitation:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
where:
\(F\) = gravitational force,
\(G\) = gravitational constant (\(6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2\)),
\(m_1\) and \(m_2\) = masses of the two objects,
\(r\) = separation between the centers of the masses.
Given:
Sally's weight (\(m_1\)) = 500.0 N,
Dog's mass (\(m_2\)) = 30 kg,
Separation (\(r\)) = 1.00 m.
Substitute the values into the formula:
\[ F = \frac{(6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2) \cdot (500.0 \, \text{N}) \cdot (30 \, \text{kg})}{(1.00 \, \text{m})^2} \]
\[ F = \frac{(6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2) \cdot 15000 \, \text{N}}{1.00 \, \text{m}} \]
\[ F \approx 1.00 \times 10^{-6} \, \text{N} \]
Therefore, the gravitational force between Sally and the dog is approximately \(1.00 \times 10^{-6} \, \text{N}\).