# Two objects have masses of #16 MG# and #22 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #5 m# to #39 m#?

The gravitational potential energy is

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The gravitational potential energy between the objects changes by 3.24 x 10^14 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.

- A model train, with a mass of #4 kg#, is moving on a circular track with a radius of #7 m#. If the train's kinetic energy changes from #8 j# to #42 j#, by how much will the centripetal force applied by the tracks change by?
- A model train, with a mass of #7 kg#, is moving on a circular track with a radius of #3 m#. If the train's rate of revolution changes from #1/3 Hz# to #2/7 Hz#, by how much will the centripetal force applied by the tracks change by?
- A model train, with a mass of #4 kg#, is moving on a circular track with a radius of #8 m#. If the train's kinetic energy changes from #6 j# to #0 j#, by how much will the centripetal force applied by the tracks change by?
- An object with a mass of #2 kg# is revolving around a point at a distance of #4 m#. If the object is making revolutions at a frequency of #4 Hz#, what is the centripetal force acting on the object?
- A model train with a mass of #2 kg# is moving along a track at #18 (cm)/s#. If the curvature of the track changes from a radius of #9 cm# to #3 cm#, by how much must the centripetal force applied by the tracks change?

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