Two objects have masses of #9 MG# and #12 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #50 m# to #230 m#?

1 Answer
Sep 21, 2017

#1.1275*10^-22J#

Explanation:

#m_1=9MG=9*10^-6 kg#
#m_2=12 MG=12*10^-6 kg#
#"Potential Energy"=-(Gm_1m_2)/r#
when #r=50m#
Potential Energy is #U_1=-(Gm_1m_2)/50#
when #r=230m#
Potential Energy is #U_2=-(Gm_1m_2)/230#

Change in Gravitational Potential Energy #=U_2-U_1#
#=-(Gm_1m_2)/230-(-(Gm_1m_2)/50)#
#=-(Gm_1m_2)/230+(Gm_1m_2)/50#
#=Gm_1m_2(1/50-1/230)#
#=6.67*10^-11(9*10^-6)(12*10^-6)((230-50)/(50*230))#
#=6.67*9*12*10^-23((180)/(50*230))#
#=11.275*10^-23J#
#=1.1275*10^-22J#