Two objects have masses of #4 MG# and #7 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #36 m# to #45 m#?

1 Answer
Pankaj Solanki
Sep 19, 2017

#1.03*10^-23J#

Explanation:

#m_1=4MG=4*10^-6 kg#
#m_2=7 MG=7*10^-6 kg#
#"Potential Energy"=-(Gm_1m_2)/r#
when #r=36m#
Potential Energy is #U_1=-(Gm_1m_2)/36#
when #r=45m#
Potential Energy is #U_2=-(Gm_1m_2)/45#

Change in Gravitational Potential Energy #=U_2-U_1#
#=-(Gm_1m_2)/45-(-(Gm_1m_2)/36)#
#=-(Gm_1m_2)/45+(Gm_1m_2)/36#
#=Gm_1m_2(1/36-1/45)#
#=6.67*10^-11(4*10^-6)(7*10^-6)((45-36)/(45*36))#
#=6.67*28*10^-23((9)/(45*36))#
#=186.76*10^-23((1)/(180))#
#=1.03*10^-23 J#

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