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Two objects have masses of #35 MG# and #21 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #8 m# to #14 m#?

Answer 1

The Gravitational potential energy between the objects change by #2.626xx10^(-13) J.#

Potential Energy #(U)=-(GMm)/r.#

G is the gravitational constant across space; M is the mass of the larger object; m is the mass of the smaller body; and r is the separation between the two objects.

#:.# Change in U #=DeltaU=U_f-U_i.# #:.DeltaU=(-(Gxx35xx21)/14)-(-(Gxx35xx21)/8) J.#

#:.Delta U=(-52.5G+91.875G)J=39.975G# Joules.

Now, #G = 6.67 xx 10^-11 Nm^2/kg^2#.

#:.Delta U=# #(39.375)xx(6.67 xx 10^-11)#. Joules #:.Delta U=262.63xx10 ^(-11)J=2.626xx10^(-13) J.# (answer).

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Answer 2

William Audy

The change in gravitational potential energy between the objects is 2.7 × 10^11 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.