Question

Two objects have masses of `6 MG` and `9 MG`. How much does the gravitational potential energy between the objects change if the distance between them changes from `320 m` to `100 m`?

Answer 1

`E_("P") = 1.72 times 10^(- 5) " J"`

Explanation:

We need to use the formula `E_("P") = - frac(G M m)(r)`; where `E_("P")` is the gravitational potential energy, `G` is the gravitational constant, `M` and `m` are the masses of the two objects, and `r` is the distance between their centres.

Let's calculate the gravitational potential energy for our case.

`r` will be the difference between the two distances:

`Rightarrow E_("P") = - frac(6.67408 times 10^(-11) " m"^(3) " kg"^(- 1) " s"^(- 2) times 6 " MG" times 9 " MG")(110 " m" - 320 " m")`

`Rightarrow E_("P") = - frac(6.67408 times 10^(-11) " m"^(3) " kg"^(- 1) " s"^(- 2) times 6000 " kg" times 9000 " kg")(- 210 " m")`

`Rightarrow E_("P") = frac(6.67408 times 10^(-11) " m"^(2) " kg"^(- 1) " s"^(- 2) times 5.4 times 10^(7) " kg"^(2))(210)`

`Rightarrow E_("P") = frac(0.0036040032 " kg m"^(2) " s"^(- 2))(210)`

`Rightarrow E_("P") = 0.00001716192 " kg m"^(2) " s"^(- 2)`

`Rightarrow E_("P") = 1.72 times 10^(- 5) " kg m"^(2) " s"^(- 2)`

`therefore E_("P") = 1.72 times 10^(- 5) " J"`

Therefore, the gravitational potential energy between the two objects is `1.72 times 10^(- 5) " J"`.