Step-by-step explanation:
To calculate the magnitude of the gravitational force exerted on the 4.20 kg baby by the 100 kg father, you can use the formula for gravitational force, which is given by Newton's law of universal gravitation:
\[F = \frac{{G \cdot (m_1 \cdot m_2)}}{{r^2}}\]
Where:
- \(F\) is the gravitational force.
- \(G\) is the gravitational constant (\(6.67430 \times 10^{-11}\, \text{N}\cdot\text{m}^2/\text{kg}^2\)).
- \(m_1\) and \(m_2\) are the masses of the two objects (in this case, the mass of the baby and the mass of the father).
- \(r\) is the distance between the centers of the two objects.
First, convert the distance to meters since it's given as 0.200 m.
Now, plug in the values:
\(F = \frac{{6.67430 \times 10^{-11}\, \text{N}\cdot\text{m}^2/\text{kg}^2 \cdot (4.20\, \text{kg} \cdot 100\, \text{kg})}}{{(0.200\, \text{m})^2}}\)
Now, calculate:
\(F ≈ 4.20 \times 10^{-8}\, \text{N}\)
So, the magnitude of the gravitational force exerted on the baby by the father is approximately \(4.20 \times 10^{-8}\, \text{N}\).