Two objects have masses of #42 MG# and #54 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #48 m# to #5 m#?

1 Answer
Y
May 10, 2017

#DeltaU=-2.71035**10^-8##"J"#

Explanation:

The formula for the gravitational potential energy between two objects is: #U=-(GMm)/r#, where #U# is the gravitational potential energy in #"J"#, #G# is the gravitational constant in #"m"^3/("s"^2"kg")#, #M# is the mass of the first object in #"kg"#, #m# is the mass of the second object #"kg"#, and #r# is the distance between the two objects in #"m"#.

Note: #G~~6.67**10^-11# #"m"^3/("s"^2"kg")#

Let #r_1# be the initial distance between the two objects and #r_2# be the final distance between the two objects:
Therefore, the change in gravitational potential energy can be written as:
#DeltaU=-(GMm)/r_2-(-(GMm)/r_1)=-GMm(1/r_2-1/r_1)#

We can substitute the given values into the equation:
#DeltaU=-(6.67**10^-11*42*54)(1/5-1/48)#
#=-2.71035**10^-8##"J"#

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