Two objects have masses of #27 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#?

1 Answer
Feb 5, 2018

It increases by #85.0%#

Explanation:

#F = G(m_1m_2/)r^2#
where G is the gravitational constant (#6.67 xx 10^(-11) m^3 s^(-2) kg^(-1))#, r is the distance between the two objects, and F is the magnitude of the force between the objects.

So, the change is inversely proportional to the square of the distance change for the same masses.
#DeltaF = Delta(1/r^2)# for the same masses.

#DeltaF = (1/54^2) – (1/32^2) = 0.0003429 – 0.0009766 = -0.0006344#
A increase of #(0.0006344 – 0.0003429)/0.0003429 xx 100 = 85.0%#