Answer :
To solve for the gravitational force between two masses, we use Newton's law of universal gravitation, which is given by the formula:
[tex]\[
F = G \frac{m_1 m_2}{r^2}
\][/tex]
Here:
- [tex]\( F \)[/tex] is the gravitational force between the two masses.
- [tex]\( G \)[/tex] is the universal 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.
- [tex]\( r \)[/tex] is the distance between the centers of the two masses.
Given:
- [tex]\( m_1 = 4.32 \, \text{kg} \)[/tex]
- [tex]\( m_2 = 163 \, \text{kg} \)[/tex]
- [tex]\( r = 83.0 \, \text{m} \)[/tex]
To calculate the gravitational force:
1. Multiply the masses of the two objects: [tex]\( m_1 \times m_2 = 4.32 \, \text{kg} \times 163 \, \text{kg} \)[/tex].
2. Divide by the square of the distance between them: [tex]\( r^2 = (83.0 \, \text{m})^2 \)[/tex].
3. Multiply the result by the gravitational constant [tex]\( G \)[/tex].
Following these steps, the calculated gravitational force is expressed in scientific notation as:
[tex]\[
F = 6.82 \times 10^{-12} \, \text{N}
\][/tex]
This means that the gravitational force between the two masses is [tex]\( 6.82 \times 10^{-12} \, \text{Newtons} \)[/tex].
[tex]\[
F = G \frac{m_1 m_2}{r^2}
\][/tex]
Here:
- [tex]\( F \)[/tex] is the gravitational force between the two masses.
- [tex]\( G \)[/tex] is the universal 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.
- [tex]\( r \)[/tex] is the distance between the centers of the two masses.
Given:
- [tex]\( m_1 = 4.32 \, \text{kg} \)[/tex]
- [tex]\( m_2 = 163 \, \text{kg} \)[/tex]
- [tex]\( r = 83.0 \, \text{m} \)[/tex]
To calculate the gravitational force:
1. Multiply the masses of the two objects: [tex]\( m_1 \times m_2 = 4.32 \, \text{kg} \times 163 \, \text{kg} \)[/tex].
2. Divide by the square of the distance between them: [tex]\( r^2 = (83.0 \, \text{m})^2 \)[/tex].
3. Multiply the result by the gravitational constant [tex]\( G \)[/tex].
Following these steps, the calculated gravitational force is expressed in scientific notation as:
[tex]\[
F = 6.82 \times 10^{-12} \, \text{N}
\][/tex]
This means that the gravitational force between the two masses is [tex]\( 6.82 \times 10^{-12} \, \text{Newtons} \)[/tex].
