Two objects have masses of #45 MG# and #36 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #48 m# to #18 m#?

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Answer 1 · 2018-04-04T15:08:31

The objects have approximately 0.00375 FEWER Joules of gravitational potential energy after they are allowed to come closer together.

The work done when displacing these two masses, #W#, is the amount that the gravitational potential changes. Note that

#W=int_48^18F(r)dr#

Where #F(r)# is the gravitational force between the two objects as a function of the distance between the objects. From Newton's Law of Gravity

#F=(Gm_1m_2)/r^2#

where

#G=# the gravitational constant #~~6.674xx10^-11m^3kg^-1s^-2#

#r=# the distance between the objects,

#m_1=# the mass of the first object = 45,000 kg, and

#m_2=# the mass of the second object = 36,000 kg.

Our integral now looks like

#W=int_48^18(Gm_1m_2)/r^2dr=Gm_1m_2int_48^18(dr)/r^2#

#W=-(Gm_1m_2)1/r# evaluated from 48 to 18.

#W=-6.674xx10^-11*45000*36000(1/18-1/48)#

#W~~-0.00375# Joules

Because this is negative, the objects have 0.00375 FEWER Joules of gravitational potential energy after they are allowed to come closer together.