Answer :
To find the gravitational force between two masses, we can use the formula for gravitational force, which is given by:
[tex]\[ F = \frac{G \times m_1 \times m_2}{r^2} \][/tex]
Where:
- [tex]\( F \)[/tex] is the gravitational force between the masses.
- [tex]\( G \)[/tex] is the gravitational constant, which is [tex]\( 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \)[/tex].
- [tex]\( m_1 \)[/tex] is the mass of the first object, in this case, [tex]\( 92.0 \, \text{kg} \)[/tex].
- [tex]\( m_2 \)[/tex] is the mass of the second object, in this case, [tex]\( 0.894 \, \text{kg} \)[/tex].
- [tex]\( r \)[/tex] is the distance between the centers of the two masses, in this case, [tex]\( 99.3 \, \text{m} \)[/tex].
Step-by-step solution:
1. Identify the Known Values:
- Mass 1 ([tex]\( m_1 \)[/tex]) = 92.0 kg
- Mass 2 ([tex]\( m_2 \)[/tex]) = 0.894 kg
- Distance ([tex]\( r \)[/tex]) = 99.3 m
- Gravitational constant ([tex]\( G \)[/tex]) = [tex]\( 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \)[/tex]
2. Substitute the Known Values into the Formula:
[tex]\[ F = \frac{6.67 \times 10^{-11} \times 92.0 \times 0.894}{(99.3)^2} \][/tex]
3. Calculate the Denominator:
Compute [tex]\( r^2 \)[/tex]:
[tex]\[ (99.3)^2 = 9850.49 \, \text{m}^2 \][/tex]
4. Calculate the Gravitational Force:
[tex]\[ F = \frac{6.67 \times 10^{-11} \times 92.0 \times 0.894}{9850.49} \][/tex]
5. Final Calculation:
- Multiply the masses and [tex]\( G \)[/tex]:
[tex]\( 6.67 \times 10^{-11} \times 92.0 \times 0.894 \approx 5.507 \times 10^{-9} \)[/tex]
- Divide by the square of the distance:
[tex]\[ F = \frac{5.507 \times 10^{-9}}{9850.49} \approx 5.563558808943573 \times 10^{-13} \, \text{N} \][/tex]
So, the gravitational force between the two masses is approximately [tex]\( 5.56 \times 10^{-13} \, \text{N} \)[/tex].
[tex]\[ F = \frac{G \times m_1 \times m_2}{r^2} \][/tex]
Where:
- [tex]\( F \)[/tex] is the gravitational force between the masses.
- [tex]\( G \)[/tex] is the gravitational constant, which is [tex]\( 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \)[/tex].
- [tex]\( m_1 \)[/tex] is the mass of the first object, in this case, [tex]\( 92.0 \, \text{kg} \)[/tex].
- [tex]\( m_2 \)[/tex] is the mass of the second object, in this case, [tex]\( 0.894 \, \text{kg} \)[/tex].
- [tex]\( r \)[/tex] is the distance between the centers of the two masses, in this case, [tex]\( 99.3 \, \text{m} \)[/tex].
Step-by-step solution:
1. Identify the Known Values:
- Mass 1 ([tex]\( m_1 \)[/tex]) = 92.0 kg
- Mass 2 ([tex]\( m_2 \)[/tex]) = 0.894 kg
- Distance ([tex]\( r \)[/tex]) = 99.3 m
- Gravitational constant ([tex]\( G \)[/tex]) = [tex]\( 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \)[/tex]
2. Substitute the Known Values into the Formula:
[tex]\[ F = \frac{6.67 \times 10^{-11} \times 92.0 \times 0.894}{(99.3)^2} \][/tex]
3. Calculate the Denominator:
Compute [tex]\( r^2 \)[/tex]:
[tex]\[ (99.3)^2 = 9850.49 \, \text{m}^2 \][/tex]
4. Calculate the Gravitational Force:
[tex]\[ F = \frac{6.67 \times 10^{-11} \times 92.0 \times 0.894}{9850.49} \][/tex]
5. Final Calculation:
- Multiply the masses and [tex]\( G \)[/tex]:
[tex]\( 6.67 \times 10^{-11} \times 92.0 \times 0.894 \approx 5.507 \times 10^{-9} \)[/tex]
- Divide by the square of the distance:
[tex]\[ F = \frac{5.507 \times 10^{-9}}{9850.49} \approx 5.563558808943573 \times 10^{-13} \, \text{N} \][/tex]
So, the gravitational force between the two masses is approximately [tex]\( 5.56 \times 10^{-13} \, \text{N} \)[/tex].
