To calculate the gravitational force \( F \) between two masses using Newton's law of universal gravitation, the formula is:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
Where:
- \( F \) is the gravitational force
- \( G \) is the gravitational constant (\( 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))
- \( m_1 \) and \( m_2 \) are the masses
- \( r \) is the distance between the centers of the two masses
From your input:
- You have \( m_1 = 2m \) and \( m_2 = 8m \).
- The distance \( r = 4 \, \text{m} \).
Now, substituting in the values:
\[ m_1 = 2m, \quad m_2 = 8m \] \[ r = 4 \, \text{m} \] \[ G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \]
Now substitute into the formula for \( F \):
\[ F = \frac{(6.67 \times 10^{-11}) \cdot (2m) \cdot (8m)}{(4)^2} \]
Calculating \( r^2 \):
\[ r^2 = 4^2 = 16 \]
Now substitute \( r^2 \) into the expression for \( F \):
\[ F = \frac{(6.67 \times 10^{-11}) \cdot (16m^2)}{16} \]
Now simplify:
\[ F = 6.67 \times 10^{-11} \cdot 2m^2 = 1.334 \times 10^{-10} m^2 \text{ N} \]
So, the gravitational force \( F \) between the two masses is:
\[ F = 1.334 \times 10^{-10} m^2 \text{ N} \]
This result depends on the mass \( m \) which was not specified in the original prompt. If you have the value of \( m \), you can substitute it to find the exact force.