Question

Two objects have masses of `6` `MG` and `8` `MG`. How much does the gravitational potential energy between the objects change if the distance between them changes from `340` `m` to `160` `m`?

Answer 1

At `340` `m` the gravitational potential energy between the masses is `-9.4xx10^-6` `J` and at `160` `m` it is `2.0xx10^-5` `J`.

The change is `-1.91xx10^-5` `J`.

Explanation:

Note that "mg" is a milligram, `10^-3` `g`, but `MG` is a megagram, `10^6` `g`. This is equal to `10^3` `kg`, and since `kg` is the `SI` unit and the gravitational constant is expressed in terms of it, that is the unit we will use.

`U=-(Gm_1m_2)/r` where `G=6.67xx10^-11` `m^3 kg^-1 s^-2`

At `340` `m`:

`U=-(Gm_1m_2)/r=-(6.67xx10^-11xx6xx10^3xx8xx10^3)/340`

`=-(3.2xx10^-3)/340=-9.4xx10^-6` `J`

At `160` `m`:

`U=-(Gm_1m_2)/r=-(6.67xx10^-11xx6xx10^3xx8xx10^3)/160`

`=-(3.2xx10^-3)/160=-2.0xx10^-5` `J`

The change is (final-initial) `=-2.0xx10^-5-(-9.4xx10^-6)=-1.91xx10^-5` `J`