Question

Object 1 with m₁ = 1.5 kg and Object 2 with m₂ = 12.5 kg are separated by r = 0.38 m.

a. Express the magnitude of the gravitational force F in terms of m₁, m₂, r, and the gravitational constant G. Express the magnitude of the gravitational force F in terms of m₁, m₂, r, and the gravitational constant G.
b. Calculate the force on the baby, in newtons, due to Jupiter (the largest planet, which has a mass of 1.90 × 10²⁷ kg) if it is at its closest distance to Earth, 6.29 × 10¹¹ m away.
c. What is the ratio of the force of the father on the baby to the force of Jupiter on the baby?

Answer 1

The magnitude of the gravitational force (F) between Object 1 and Object 2 is given by F = G * (m₁ * m₂) / r². The force on the baby due to Jupiter at its closest distance is approximately 8.44 × 10¹⁸ N. The ratio of the force of the father on the baby to the force of Jupiter on the baby is approximately 2.96 × 10¹³.

Step-by-step explanation:

In physics, the gravitational force (F) between two objects is given by Newton's law of gravitation:
`\(F = (G \cdot m_1 \cdot m_2)/(r^2)\),` where
`\(G\)` is the gravitational constant
`(approximately \(6.67 *`
`10^(-11) \, \text{N} \cdot \text{m}^2/\text{kg}^2\)), \(m_1\) and \(m_2\)` are the masses of the objects, and \(r\) is the separation between their centers.

For part (a), the expression for the gravitational force between Object 1 and Object 2 is derived from this formula:
`\(F = G \cdot (m_1 \cdot m_2)/(r^2)\)`.

For part (b), the force on the baby due to Jupiter is calculated using the same gravitational force formula, with
`\(m_1\)`as the mass of the baby,
`(m_2)`as the mass of Jupiter
`(given as`
`\(1.90 * 10^(27) \, \text{kg}\))`, and
`\(r\)` as the closest distance between Earth and Jupiter
`(6.29 * 10^(11) \, \text{m}\))`.

For part (c), the ratio of forces is found by dividing the force of the father on the baby by the force of Jupiter on the baby.