Question

Two objects have masses of `3 MG` and `10 MG`. How much does the gravitational potential energy between the objects change if the distance between them changes from `130 m` to `24 m`?

Answer 1

`=-6.79*10^-23J`

Explanation:

`m_1=3MG=3*10^-6 kg`
`m_2=10 MG=10*10^-6 kg`
`"Gravitational Potential Energy"=-(Gm_1m_2)/r`
when `r=130m`
Potential Energy is `U_1=-(Gm_1m_2)/130`
when `r=24m`
Potential Energy is `U_2=-(Gm_1m_2)/24`

Change in Gravitational Potential Energy `=U_2-U_1`
`=-(Gm_1m_2)/24-(-(Gm_1m_2)/130)`
`=-(Gm_1m_2)/24+(Gm_1m_2)/130`
`=Gm_1m_2(1/130-1/24)`
`=6.67*10^-11(3*10^-6)(10*10^-6)((24-130)/(24*130))`
`=6.67*3*10*10^-23((-106)/(24*130))`
`=-6.79*10^-23J`