Question

Two objects have masses of `24 MG` and `42 MG`. How much does the gravitational potential energy between the objects change if the distance between them changes from `54 m` to `32 m`?

Answer 1

40 yN

Explanation:

`F_1 = -G(m_1m_2)/(r_1^2) and F_2 = -G(m_1m_2)/(r_2^2)`

Therefore,
`Delta F = F_1 - F_2 = -Gm_1m_2 * (1/r_1^2 - 1/r_2^2)`

Using the values supplied, we get
`Delta F = -(6.67 * 10^-11 Nm^2/kg^2) * (24 mg) * (42 mg) * (1/(54 m )^2 - 1/(32 m)^2) = 4 * 10^-23 N`

So the force increases by 40 yoctonewtons.