# A model train with a mass of #9 kg# is moving along a track at #15 (cm)/s#. If the curvature of the track changes from a radius of #45 cm# to #30 cm#, by how much must the centripetal force applied by the tracks change?

The change in centripetal force is

The centripetal force is

The variation in centripetal force is

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The centripetal force applied by the tracks must increase by approximately 1.44 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 #5 kg# is moving along a track at #14 (cm)/s#. If the curvature of the track changes from a radius of #84 cm# to #21 cm#, by how much must the centripetal force applied by the tracks change?
- The force of gravity depends on what two variables?
- A model train, with a mass of #8 kg#, is moving on a circular track with a radius of #2 m#. If the train's kinetic energy changes from #72 j# to #36 j#, by how much will the centripetal force applied by the tracks change by?
- A model train, with a mass of #12 kg#, is moving on a circular track with a radius of #9 m#. If the train's kinetic energy changes from #18 j# to #27 j#, 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 #24 (cm)/s#. If the curvature of the track changes from a radius of #96 cm# to #360 cm#, by how much must the centripetal force applied by the tracks change?

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