# A model train, with a mass of #4 kg#, is moving on a circular track with a radius of #15 m#. If the train's kinetic energy changes from #96 j# to #48 j#, by how much will the centripetal force applied by the tracks change by?

The change in centripetal force is

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 96 J.

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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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