Questions: Two masses are 5.60 m apart. Mass 1 is 4.17 kg and mass 2 is 3.29 kg. What is the gravitational force between the two masses? F=[?] × 10^[?] N G=6.67 × 10^-11 N · m^2 / kg^2

Two masses are 5.60 m apart. Mass 1 is 4.17 kg and mass 2 is 3.29 kg.

What is the gravitational force between the two masses?

F=[?] × 10^[?] N

G=6.67 × 10^-11 N · m^2 / kg^2

Transcript text: Two masses are 5.60 m apart. Mass 1 is 4.17 kg and mass 2 is 3.29 kg . What is the gravitational force between the two masses? \[ \begin{array}{l} \vec{F}=[?] \times 10^{[?]} \mathrm{N} \\ \mathrm{G}=6.67 \times 10^{-11} \mathrm{~N} \cdot \mathrm{~m}^{2} / \mathrm{kg}^{2} \end{array} \]

Solution

Solution Steps

Step 1: Identify the Given Values

We are given:

Distance between the masses, \( r = 5.60 \) m
Mass 1, \( m_1 = 4.17 \) kg
Mass 2, \( m_2 = 3.29 \) kg
Gravitational constant, \( G = 6.67 \times 10^{-11} \) N·m\(^2\)/kg\(^2\)

Step 2: Write the Gravitational Force Formula

The gravitational force \( F \) between two masses is given by Newton's law of gravitation: \[ F = \frac{G m_1 m_2}{r^2} \]

Step 3: Substitute the Given Values into the Formula

Substitute the given values into the formula: \[ F = \frac{(6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2) \times (4.17 \, \text{kg}) \times (3.29 \, \text{kg})}{(5.60 \, \text{m})^2} \]

Step 4: Calculate the Numerator

Calculate the product of \( G \), \( m_1 \), and \( m_2 \): \[ 6.67 \times 10^{-11} \times 4.17 \times 3.29 = 9.1677 \times 10^{-10} \]

Step 5: Calculate the Denominator

Calculate the square of the distance \( r \): \[ (5.60)^2 = 31.36 \]

Step 6: Compute the Gravitational Force

Divide the numerator by the denominator to find \( F \): \[ F = \frac{9.1677 \times 10^{-10}}{31.36} = 2.924 \times 10^{-11} \, \text{N} \]