Two objects have masses of #4 MG# and #8 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #150 m# to #450 m#?

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Answer 1 · 2017-03-05T21:05:31

#8.45xx10^-8N#

Gravitational potential energy between two object is given by

#U = G(m_1m_2)/r^2#

where #U# is the gravitational potential energy, #G=6.67xx10^-11#, #m# is the mass, and #r# is the distance between them.

Notice it is the same equation as for gravitational force.

Put the values in the question into the equation, so the initial G.P.E is

#U = 6.67xx10^-11 xx (4xx10^3 xx 8 xx 10^3)/150^2 = 9.5xx10^-8N#

The final G.P.E after the objects have moved apart will be

#U = 6.67xx10^-11 xx (4xx10^3 xx 8xx10^3)/450^2 = 1.05xx10^-8N#

Therefore, the total change in the G.P.E is

#9.5xx10^-8 - 1.05xx10^-8 = 8.45xx10^-8N#