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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#?

Answer 1

It increases by #85.0%#

#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%#

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Answer 2

Xavier Adame

The change in gravitational potential energy between the objects is (4.19 \times 10^{15}) joules.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.