Two objects have masses of #9 MG# and #7 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #36 m# to #45 m#?
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"How to prove this ?
#2|k^2# then #2|k# for some #k\inZZ#"
Answer: #2.3345**10^-11##"J"#
A very similarly worded problem .
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 #6.67*10^-11"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*9*7)(1/45-1/36)#
#=2.3345**10^-11##"J"#
