Question

Two spheres have a gravitational force between
them of 45 N. If the distance between the masses
is increased to 4.0 times its original distance, what
is the new force?

Answer 1

Answer:

The new force is 2.8125 N

Explanation:

Newton’s Law of Universal Gravitation

Objects attract each other with a force that is proportional to their masses and inversely proportional to the square of the distance.  

$\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}}$

Where:

m1 = mass of object 1

m2 = mass of object 2

r     = distance between the objects' center of masses

G   = gravitational constant: 6.67\cdot 10^{-11}~Nw*m^2/Kg^2

Suppose two spheres have a gravitational force between them of F = 45 N. Now increase the distance to r'=4r. The new force F' is:

$\displaystyle F'=G{\frac {m_{1}m_{2}}{(4r)^{2}}}$

$\displaystyle F'=G{\frac {m_{1}m_{2}}{16r^{2}}}$

$\displaystyle F'=\frac{1}{16}\ G{\frac {m_{1}m_{2}}{r^{2}}}$

Substituting the original value of the force:

$\displaystyle F'=\frac{1}{16}\ 45 N$

F' = 2.8125 N

The new force is 2.8125 N