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#?

Answer 1

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"#
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Answer 2

The change in gravitational potential energy is ( -2.52 \times 10^{13} \ \text{J} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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