Two objects have masses of 9 MG and 7 MG. How much does the gravitational potential energy between the objects change if the distance between them changes from 36 m to 45 m?

1 Answer
May 12, 2017

Answer: 2.3345**10^-11"J"

Explanation:

A very similarly worded problem .

The formula for the gravitational potential energy between two objects is: U=-(GMm)/r, where U is the gravitational potential energy in "J", G is the gravitational constant 6.67*10^-11"m"^3/("s"^2"kg"), M is the mass of the first object in "kg", m is the mass of the second object "kg", and r is the distance between the two objects in "m".

Note: G~~6.67**10^-11 "m"^3/("s"^2"kg")

Let r_1 be the initial distance between the two objects and r_2 be the final distance between the two objects:
Therefore, the change in gravitational potential energy can be written as:
DeltaU=-(GMm)/r_2-(-(GMm)/r_1)=-GMm(1/r_2-1/r_1)

We can substitute the given values into the equation:
DeltaU=-(6.67**10^-11*9*7)(1/45-1/36)
=2.3345**10^-11"J"