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

The new force is 2.8125 N

Step-by-step 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'=(1)/(16)\ G{\frac {m_(1)m_(2)}{r^(2)}}`

Substituting the original value of the force:

`\displaystyle F'=(1)/(16)\ 45 N`

F' = 2.8125 N

The new force is 2.8125 N