Answer :
To find the gravitational force between two masses, we use the formula for gravitational force:
[tex]\[ F = G \times \frac{{m_1 \times m_2}}{{r^2}} \][/tex]
where:
- [tex]\( F \)[/tex] is the gravitational force,
- [tex]\( G \)[/tex] is the gravitational constant, approximately [tex]\( 6.67430 \times 10^{-11} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2} \)[/tex],
- [tex]\( m_1 \)[/tex] and [tex]\( m_2 \)[/tex] are the masses of the two objects, and
- [tex]\( r \)[/tex] is the distance between the centers of the two masses.
Given:
- [tex]\( m_1 = 92.0 \, \text{kg} \)[/tex]
- [tex]\( m_2 = 0.894 \, \text{kg} \)[/tex]
- [tex]\( r = 99.3 \, \text{m} \)[/tex]
Step-by-step Calculation:
1. Multiply the masses:
[tex]\( m_1 \times m_2 = 92.0 \times 0.894 = 82.248 \, \text{kg}^2 \)[/tex]
2. Square the distance:
[tex]\( r^2 = (99.3)^2 = 9860.49 \, \text{m}^2 \)[/tex]
3. Calculate the gravitational force using the formula:
[tex]\[ F = 6.67430 \times 10^{-11} \times \frac{{82.248}}{{9860.49}} \][/tex]
Performing this calculation gives the force [tex]\( F \approx 5.5671455110243 \times 10^{-13} \, \text{N} \)[/tex].
4. Scale the force for the output format:
To fit the format [tex]\(\overrightarrow{F}=[?] \times 10^{[?]} \, \text{N}\)[/tex], multiply the calculated force by [tex]\( 10^{11} \)[/tex] so it appears in a more readable scientific format.
[tex]\[ F \text{ (scaled)} \approx 0.055671455110243 \times 10^{-2} \, \text{N} \][/tex]
Conclusion:
The gravitational force between the two masses, when formatted, is approximately:
[tex]\[
\overrightarrow{F} = 0.055671455110243 \times 10^{-2} \, \text{N}
\][/tex]
This represents a very small gravitational force due to the small masses and large distance apart, which is typical for everyday objects.
[tex]\[ F = G \times \frac{{m_1 \times m_2}}{{r^2}} \][/tex]
where:
- [tex]\( F \)[/tex] is the gravitational force,
- [tex]\( G \)[/tex] is the gravitational constant, approximately [tex]\( 6.67430 \times 10^{-11} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2} \)[/tex],
- [tex]\( m_1 \)[/tex] and [tex]\( m_2 \)[/tex] are the masses of the two objects, and
- [tex]\( r \)[/tex] is the distance between the centers of the two masses.
Given:
- [tex]\( m_1 = 92.0 \, \text{kg} \)[/tex]
- [tex]\( m_2 = 0.894 \, \text{kg} \)[/tex]
- [tex]\( r = 99.3 \, \text{m} \)[/tex]
Step-by-step Calculation:
1. Multiply the masses:
[tex]\( m_1 \times m_2 = 92.0 \times 0.894 = 82.248 \, \text{kg}^2 \)[/tex]
2. Square the distance:
[tex]\( r^2 = (99.3)^2 = 9860.49 \, \text{m}^2 \)[/tex]
3. Calculate the gravitational force using the formula:
[tex]\[ F = 6.67430 \times 10^{-11} \times \frac{{82.248}}{{9860.49}} \][/tex]
Performing this calculation gives the force [tex]\( F \approx 5.5671455110243 \times 10^{-13} \, \text{N} \)[/tex].
4. Scale the force for the output format:
To fit the format [tex]\(\overrightarrow{F}=[?] \times 10^{[?]} \, \text{N}\)[/tex], multiply the calculated force by [tex]\( 10^{11} \)[/tex] so it appears in a more readable scientific format.
[tex]\[ F \text{ (scaled)} \approx 0.055671455110243 \times 10^{-2} \, \text{N} \][/tex]
Conclusion:
The gravitational force between the two masses, when formatted, is approximately:
[tex]\[
\overrightarrow{F} = 0.055671455110243 \times 10^{-2} \, \text{N}
\][/tex]
This represents a very small gravitational force due to the small masses and large distance apart, which is typical for everyday objects.
