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.
