Two objects have masses of #32 MG# and #36 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #42 m# to #18 m#?

1 Answer
Jan 31, 2018

The change in gravitational energy is #=91.47*10^-5J#

Explanation:

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 mass causing the field is #=M_1 kg# and #=M_2 kg#

The mass is #M_1=32MG=32*10^6g=32*10^3kg#

The mass is #M_2=36MG=36*10^6g=36*10^3kg#

The distance between the centers is #=Rm#

The distance #R_1=42m#

The distance #R_2=18m#

Therefore,

#Phi_1=(-G*(32*10^3*36*10^3)/42)#

#Phi_2=(-G*(32*10^3*36*10^3)/28)#

So,

#Phi_1-Phi_2=(-G*(32*10^3*36*10^3)/42)-(-G*(32*10^3*36*10^3)/28)#

#=32*36*10^6*6.67*10^-11(1/28-1/42)#

#=91.47*10^-5J#