# 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 rate of revolution changes from #5/8 Hz# to #1/4 Hz#, by how much will the centripetal force applied by the tracks change by?

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 can be calculated using the formula ( F = m \cdot \omega^2 \cdot r ), where ( m ) is the mass of the train, ( \omega ) is the angular velocity, and ( r ) is the radius of the circular track.

Initially, when the rate of revolution is ( \frac{5}{8} ) Hz, the angular velocity ( \omega_1 ) can be calculated using the formula ( \omega_1 = 2\pi f_1 ), where ( f_1 ) is the frequency. ( \omega_1 = 2\pi \left(\frac{5}{8}\right) )

Similarly, when the rate of revolution is ( \frac{1}{4} ) Hz, the angular velocity ( \omega_2 ) can be calculated using the same formula. ( \omega_2 = 2\pi \left(\frac{1}{4}\right) )

Now, the change in centripetal force can be calculated as: ( \Delta F = m \cdot (\omega_2^2 - \omega_1^2) \cdot r )

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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 #6 kg#, is moving on a circular track with a radius of #2 m#. If the train's rate of revolution changes from #4 Hz# to #6 Hz#, by how much will the centripetal force applied by the tracks change by?
- A model train, with a mass of #6 kg#, is moving on a circular track with a radius of #2 m#. If the train's kinetic energy changes from #27 j# to #36 j#, by how much will the centripetal force applied by the tracks change by?
- A model train with a mass of #3 kg# is moving along a track at #8 (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 #8 kg#, is moving on a circular track with a radius of #2 m#. If the train's kinetic energy changes from #36 j# to #48 j#, 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 #21 j#, by how much will the centripetal force applied by the tracks change by?

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