Two objects have masses of #4 MG# and #18 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #7 m# to #2 m#?

Answer 1

Nathan Ashcroft

The gravitational eneregy changes by #=4.81*10^-3J#

Gravitational potential is the potential energy per kilogram at a point in a field.

So the units are #J, "Joules"#

#Phi=-G(M_1M_2)/R#

The gravitational universal constant is

#G=6.67*10^-11Nm^2kg^-2#

The masses causing the field is #=M_1 kg# and #=M_2 kg#

The mass is #M_1=4MG=4*10^6g=4*10^3kg#

The mass is #M_2=18MG=18*10^6g=18*10^3kg#

The distance between the centers is #=Rm#

The distance #R_1=7m#

The distance #R_2=2m#

Therefore,

#Phi_1=(-G*(4*10^3*18*10^3)/7)#

#Phi_2=(-G*(4*10^3*18*10^3)/2)#

So,

#Phi_1-Phi_2=(-G*(4*10^3*18*10^3)/7)-(-G*(4*10^3*18*10^3)/2)#

#=4*18*10^6*6.67*10^-11(1/2-1/7)#

#=480.6*10^-5J#

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Answer 2

Julia Aguilar

The gravitational potential energy between the objects changes by approximately 1.71 x 10^14 joules.

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