# A model train, with a mass of #8# #kg#, is moving on a circular track with a radius of #1# #m#. If the train's kinetic energy changes from #32# #J# to #0# #J#, by how much will the centripetal force applied by the tracks change?

The centripetal force is given by

Since there is no remaining kinetic energy, there is also no remaining velocity.

To determine the initial velocity, we can use the mass, radius, and initial kinetic energy as follows:

The initial centripetal force will be: Since the final velocity is zero, the final centripetal force will also be zero.

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The centripetal force will decrease by 32 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 #8 kg#, is moving on a circular track with a radius of #5 m#. If the train's kinetic energy changes from #72 j# to #0 j#, by how much will the centripetal force applied by the tracks change by?
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- A model train, with a mass of #8 kg#, is moving on a circular track with a radius of #6 m#. If the train's rate of revolution changes from #5/3 Hz# to #1/4 Hz#, by how much will the centripetal force applied by the tracks change by?
- A model train, with a mass of #32 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?
- An object with a mass of #2 kg# is revolving around a point at a distance of #5 m#. If the object is making revolutions at a frequency of #4 Hz#, what is the centripetal force acting on the object?

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