Question

Two objects have masses of `32 MG` and `36 MG`. How much does the gravitational potential energy between the objects change if the distance between them changes from `42 m` to `18 m`?

Answer 1

The change in gravitational energy is `=91.47*10^-5J`

Explanation:

Gravitational potential is the potential energy per kilogram at a point in a field.

So the units are `J, "Joules"`

`Phi=-G(M_1M_2)/R`

The gravitational universal constant is

`G=6.67*10^-11Nm^2kg^-2`

The mass causing the field is `=M_1 kg` and `=M_2 kg`

The mass is `M_1=32MG=32*10^6g=32*10^3kg`

The mass is `M_2=36MG=36*10^6g=36*10^3kg`

The distance between the centers is `=Rm`

The distance `R_1=42m`

The distance `R_2=18m`

Therefore,

`Phi_1=(-G*(32*10^3*36*10^3)/42)`

`Phi_2=(-G*(32*10^3*36*10^3)/28)`

So,

`Phi_1-Phi_2=(-G*(32*10^3*36*10^3)/42)-(-G*(32*10^3*36*10^3)/28)`

`=32*36*10^6*6.67*10^-11(1/28-1/42)`

`=91.47*10^-5J`