A model train, with a mass of #2 kg#, is moving on a circular track with a radius of #6 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 increases by
Because the inputs (kinetic energy) and the outputs (centripetal force) don't seem to be related, there must be a link, which we can find by first writing down the equations for each. This is the kind of question that looks complicated when you read it but is simple when you break it down into small steps:
additionally
As a result, the centripetal force in the initial and final states can be obtained from:
additionally
Thus, the difference between these two forces represents the change in centripetal force:
Delta F_c is equal to F_(c2)-F_(c1), or 32N -2/3N = 31 1/3N.
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The centripetal force applied by the tracks will change by 192 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.
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 #2 kg# is moving along a track at #2 (cm)/s#. If the curvature of the track changes from a radius of #7 cm# to #12 cm#, by how much must the centripetal force applied by the tracks change?
- An object with a mass of #5 kg# is revolving around a point at a distance of #3 m#. If the object is making revolutions at a frequency of #17 Hz#, what is the centripetal force acting on the object?
- A model train with a mass of #2 kg# is moving along a track at #9 (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?
- A model train, with a mass of #3 kg#, is moving on a circular track with a radius of #2 m#. If the train's rate of revolution changes from #5/4 Hz# to #1/8 Hz#, by how much will the centripetal force applied by the tracks change by?
- 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 #0 j#, by how much will the centripetal force applied by the tracks change by?

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