Answer :
To find the gravitational force between two masses, you can use Newton's law of universal gravitation. According to this law, the gravitational force ([tex]\( F \)[/tex]) between two masses is given by the formula:
[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 involved,
- [tex]\( r \)[/tex] is the distance between the centers of the two masses.
Given:
- Mass 1 ([tex]\( m_1 \)[/tex]) = 92.0 kg,
- Mass 2 ([tex]\( m_2 \)[/tex]) = 0.894 kg,
- Distance ([tex]\( r \)[/tex]) = 99.3 meters.
Let's plug these values into the formula:
1. Multiply the masses:
[tex]\[ 92.0 \, \text{kg} \times 0.894 \, \text{kg} = 82.248 \, \text{kg}^2 \][/tex]
2. Calculate the square of the distance:
[tex]\[ (99.3 \, \text{m})^2 = 9852.49 \, \text{m}^2 \][/tex]
3. Use the value of [tex]\( G \)[/tex] to find the force:
[tex]\[ F = 6.67430 \times 10^{-11} \, \text{m}^3\,\text{kg}^{-1}\,\text{s}^{-2} \times \frac{82.248 \, \text{kg}^2}{9852.49 \, \text{m}^2} \][/tex]
4. Solve for [tex]\( F \)[/tex]:
[tex]\[ F \approx 5.5671455110243 \times 10^{-13} \, \text{N} \][/tex]
Now, to express the gravitational force in the form [tex]\(\overrightarrow{F}=[?] \times 10^{[?]} \, \text{N}\)[/tex], we split the force into its coefficient and exponent:
- The coefficient is approximately [tex]\( 5.567145511024299 \)[/tex].
- The exponent is [tex]\(-13\)[/tex].
Thus, the gravitational force between the two masses is approximately:
[tex]\[ \overrightarrow{F} = 5.567145511024299 \times 10^{-13} \, \text{N} \][/tex]
[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 involved,
- [tex]\( r \)[/tex] is the distance between the centers of the two masses.
Given:
- Mass 1 ([tex]\( m_1 \)[/tex]) = 92.0 kg,
- Mass 2 ([tex]\( m_2 \)[/tex]) = 0.894 kg,
- Distance ([tex]\( r \)[/tex]) = 99.3 meters.
Let's plug these values into the formula:
1. Multiply the masses:
[tex]\[ 92.0 \, \text{kg} \times 0.894 \, \text{kg} = 82.248 \, \text{kg}^2 \][/tex]
2. Calculate the square of the distance:
[tex]\[ (99.3 \, \text{m})^2 = 9852.49 \, \text{m}^2 \][/tex]
3. Use the value of [tex]\( G \)[/tex] to find the force:
[tex]\[ F = 6.67430 \times 10^{-11} \, \text{m}^3\,\text{kg}^{-1}\,\text{s}^{-2} \times \frac{82.248 \, \text{kg}^2}{9852.49 \, \text{m}^2} \][/tex]
4. Solve for [tex]\( F \)[/tex]:
[tex]\[ F \approx 5.5671455110243 \times 10^{-13} \, \text{N} \][/tex]
Now, to express the gravitational force in the form [tex]\(\overrightarrow{F}=[?] \times 10^{[?]} \, \text{N}\)[/tex], we split the force into its coefficient and exponent:
- The coefficient is approximately [tex]\( 5.567145511024299 \)[/tex].
- The exponent is [tex]\(-13\)[/tex].
Thus, the gravitational force between the two masses is approximately:
[tex]\[ \overrightarrow{F} = 5.567145511024299 \times 10^{-13} \, \text{N} \][/tex]
