Question

Two objects have masses of `45 MG` and `54 MG`. How much does the gravitational potential energy between the objects change if the distance between them changes from `48 m` to `16 m`?

Answer 1

`DeltaU=-6.75338**10^-9` `"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 in `"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*45*54)(1/16-1/48)`
`=-6.75338**10^-9` `"J"`