Question

Two objects have masses of `17 MG` and `22 MG`. How much does the gravitational potential energy between the objects change if the distance between them changes from `55 m` to `32 m`?

Answer 1

It is increased by 72%

Explanation:

The gravitational potential energy is

`U = -G(m_1*m_2)/r`

where G `=6.67 xx 10^-11 (Nm)/(kg^2)`is the universal gravitational constant, `m_1 and m_2` are masses, and r is the separation between`m_1 and m_2.` Any objects that attract each other have negative potential energy; otherwise, objects that repel each other has positive potential energy.

Hence, when the distance between shrinks, the gravitation energy becomes stronger (or more negative).

Let
`U_1 = -G(m_1*m_2)/r_1 = -G( 17MG*22MG)/(55m)`

`U_2 = -G(m_1*m_2)/r_2 = -G( 17MG*22MG)/(32m)`

You calculate the potential energies above explicitly if you wish by substituting G with the numerical value given above, and then find their difference.

Or you can compare the final to the initial potential energy to get
:
`U_2/U_1= 55/32`

Then
`U_2 = 55/32U_1`

That is, the potential has become 1.72x stronger than before.

The change is:
`Delta U= U_2-U_1 = 55/32 U_1 - U_1 = 23/32U_1`

The percentage change is:

`(Delta U)/U_1 xx100% = 23/32 xx 100% =72%`

Thus the potential energy is 72% stronger then before.