# 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?

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 9 newtons.

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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 #6 (cm)/s#. If the curvature of the track changes from a radius of #56 cm# to #48 cm#, by how much must the centripetal force applied by the tracks change?
- A model train with a mass of #8 kg# is moving along a track at #9 (cm)/s#. If the curvature of the track changes from a radius of #180 cm# to #81 cm#, by how much must the centripetal force applied by the tracks change?
- In the figure, a 1.91 kg ball is connected by means of two massless strings, each of length L = 1.06 m, to a vertical, rotating rod. The strings are tied to the rod with separation d = 1.06 m and are taut. The tension in the upper string is 50.0 N ?
- A model train with a mass of #2 kg# is moving along a track at #15 (cm)/s#. If the curvature of the track changes from a radius of #5 cm# to #12 cm#, by how much must the centripetal force applied by the tracks change?
- A washing machine has a fast spin cycle of 542 rev/min and a slow spin cycle of 328 rev/min. The diameter of the washing machine drum is 0.43 m. What is the ratio of the centripetal accelerations for the spin cycles?

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