# A model train, with a mass of #5 kg#, is moving on a circular track with a radius of #3 m#. If the train's rate of revolution changes from #1/2 Hz# to #2/8 Hz#, by how much will the centripetal force applied by the tracks change by?

The change in centripetal force is

Centripetal force is what

The frequencies that are

The centripetal force fluctuation is

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The centripetal force applied by the tracks will change by a factor of 4, increasing.

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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 #2 kg# is moving along a track at #36 (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?
- A model train with a mass of #3 kg# is moving along a track at #16 (cm)/s#. If the curvature of the track changes from a radius of #8 cm# to #32 cm#, by how much must the centripetal force applied by the tracks change?
- A model train, with a mass of #2 kg#, is moving on a circular track with a radius of #4 m#. If the train's rate of revolution changes from #1/2 Hz# to #2/8 Hz#, by how much will the centripetal force applied by the tracks change by?
- A model train with a mass of #1 kg# is moving along a track at #6 (cm)/s#. If the curvature of the track changes from a radius of #8 cm# to #9 cm#, by how much must the centripetal force applied by the tracks change?
- Two objects have masses of #5 MG# and #7 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #90 m# to #2000 m#?

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