# Two objects have masses of #3 MG# and #15 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #160 m# to #280 m#?

See the explanation below

HINT:

Now, substitute the corresponding values in above formula to get change in potential energy.

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The change in gravitational potential energy between the two objects when the distance between them changes from 160 m to 280 m can be calculated using the formula:

ΔU = G * m1 * m2 * (1/r2 - 1/r1)

where: ΔU is the change in gravitational potential energy, G is the gravitational constant (6.674 × 10^(-11) N m^2/kg^2), m1 and m2 are the masses of the objects (3 MG and 15 MG respectively), and r1 and r2 are the initial and final distances between the objects (160 m and 280 m respectively).

Substituting the given values into the formula:

ΔU = (6.674 × 10^(-11) N m^2/kg^2) * (3 × 10^6 kg) * (15 × 10^6 kg) * (1/280 - 1/160)

ΔU ≈ -2.68 × 10^8 J

Therefore, the change in gravitational potential energy between the objects is approximately -2.68 × 10^8 Joules.

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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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