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

Here, the centripetal force is from the tracks keeping the train in a circle.

Finding the difference in force

Substituting in values

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The centripetal force applied by the tracks will decrease by approximately 16 N.

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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 along a track at #21 (cm)/s#. If the curvature of the track changes from a radius of #84 cm# to #140 cm#, by how much must the centripetal force applied by the tracks change?
- Two objects have masses of #36 MG# and #18 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #81 m# to #3 m#?
- A model train with a mass of #3 kg# is moving along a track at #12 (cm)/s#. If the curvature of the track changes from a radius of #5 cm# to #24 cm#, by how much must the centripetal force applied by the tracks change?
- An object with a mass of #6 kg# is revolving around a point at a distance of #8 m#. If the object is making revolutions at a frequency of #3 Hz#, what is the centripetal force acting on the object?
- A model train with a mass of #9 kg# is moving along a track at #18 (cm)/s#. If the curvature of the track changes from a radius of #24 cm# to #42 cm#, by how much must the centripetal force applied by the tracks change?

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