Two objects have masses of #16 MG# and #27 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #25 m# to #32 m#?

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Answer 1 · 2016-06-05T20:16:33

It changes of #3.78# J.

The gravitational potential energy between two masses #M_1# and #M_2# at distance #r# is

#U=-(GM_1M_2)/r#.

The difference in energy is

#\Delta U=-(GM_1M_2)/r_f+(GM_1M_2)/r_i#

#=GM_1M_2(1/r_i-1/r_f)#

Substituting the numbers and observing that the mass is expressed in units of #G#, we have

#=16*27(1/25-1/32)=16*27*7/800#

#=189/50\approx3.78# J