College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Two masses are 83.0 m apart. Mass 1 is 4.32 kg and mass 2 is 163 kg. What is the gravitational force between the two masses?

\[ \vec{F} = G \frac{m_1 m_2}{r^2} \]

where

\[ G = 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2 / \text{kg}^2 \]

\[ \vec{F} = [?] \times 10^{[?]} \, \text{N} \]

Answer :

To determine the gravitational force between two masses, you can use Newton's law of universal gravitation, which is formulated as follows:

[tex]\[ \vec{F} = G \frac{m_1 m_2}{r^2} \][/tex]

Given:
- [tex]\( G \)[/tex] (Gravitational constant) = [tex]\( 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2 / \text{kg}^2 \)[/tex]
- [tex]\( m_1 \)[/tex] (Mass 1) = [tex]\( 4.32 \, \text{kg} \)[/tex]
- [tex]\( m_2 \)[/tex] (Mass 2) = [tex]\( 163 \, \text{kg} \)[/tex]
- [tex]\( r \)[/tex] (Distance between the masses) = [tex]\( 83.0 \, \text{m} \)[/tex]

Step-by-step solution:

1. Identify the masses and the separation distance:

[tex]\[ m_1 = 4.32 \, \text{kg} \][/tex]
[tex]\[ m_2 = 163 \, \text{kg} \][/tex]
[tex]\[ r = 83.0 \, \text{m} \][/tex]

2. Substitute the values into the formula for the gravitational force:

[tex]\[
\vec{F} = 6.67 \times 10^{-11} \cdot \frac{4.32 \times 163}{83.0^2}
\][/tex]

3. Calculate the gravitational force:

- First, calculate the product of the masses:

[tex]\[ m_1 \times m_2 = 4.32 \times 163 = 704.16 \, \text{kg}^2 \][/tex]

- Next, calculate the square of the distance:

[tex]\[ r^2 = 83.0^2 = 6889.0 \, \text{m}^2 \][/tex]

- Now, substitute these intermediate results back into the formula:

[tex]\[
\vec{F} = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \cdot \frac{704.16 \, \text{kg}^2}{6889.0 \, \text{m}^2}
\][/tex]

- Simplify the division inside the parentheses:

[tex]\[ \frac{704.16}{6889.0} \approx 0.1022 \][/tex]

- Finally, multiply by the gravitational constant:

[tex]\[ 6.67 \times 10^{-11} \cdot 0.1022 \approx 6.82 \times 10^{-12} \, \text{N} \][/tex]

Thus, the gravitational force between the two masses is approximately:

[tex]\[ \vec{F} \approx 6.82 \times 10^{-12} \, \text{N} \][/tex]