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 `18 m`?

Answer 1

As the distance between the objects decreases, the gravitational force increases.

Explanation:

Given/Known:

The mass must be converted from mg to kg.

`m_1=45"mg"xx(1"g")/(1000"mg")xx(1"kg")/(1000"g")="0.000045 kg"`

`m_2="0.000054 kg"`

`d_1="48 m"`

`d_2="18 m"`

Universal gravitation constant, G `=` `6.67xx10^(-11)"N"*"m"^2"/kg"^2`

Equation:

`"F"_"grav"="G"((m_1m_2)/(d^2))`

Gravitational force at 48 m

`"F"_"grav"=(6.67xx10^(-11) ("N"*color(red)cancel(color(black)("m"^2)))/color(red)cancel(color(black)("kg"^2))xx0.000045color(red)cancel(color(black)("kg"))xx0.000054color(red)cancel(color(black)("kg")))/(48color(red)cancel(color(black)("m"^2)))=7.0xx10^(-23)" N"`

Gravitational force at 18 m
`"F"_"grav"=(6.67xx10^(-11) ("N"*color(red)cancel(color(black)("m"^2)))/color(red)cancel(color(black)("kg"^2))xx0.000045color(red)cancel(color(black)("kg"))xx0.000054color(red)cancel(color(black)("kg")))/(18color(red)cancel(color(black)("m"^2)))=5.0xx10^(-22)" N"`