# 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 kinetic energy changes from #2 j# to #96 j#, by how much will the centripetal force applied by the tracks change by?

The centripetal force change by

The centripetal force is

The kinetic energy is

The variation of kinetic energy is

The variation of centripetal force is

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The centripetal force applied by the tracks will change by 94 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 #1 kg# is moving along a track at #24 (cm)/s#. If the curvature of the track changes from a radius of #72 cm# to #150 cm#, by how much must the centripetal force applied by the tracks change?
- 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 #42 cm# to #45 cm#, by how much must the centripetal force applied by the tracks change?
- A model train, with a mass of #15 kg#, is moving on a circular track with a radius of #6 m#. If the train's kinetic energy changes from #40 j# to #27 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 #6 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 #24 kg#, is moving on a circular track with a radius of #3 m#. If the train's kinetic energy changes from #18 j# to #21 j#, by how much will the centripetal force applied by the tracks change by?

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