# A model train with a mass of #4 kg# is moving along a track at #9 (cm)/s#. If the curvature of the track changes from a radius of #36 cm# to #24 cm#, by how much must the centripetal force applied by the tracks change?

The change in centripetal force is

The centripetal force is

The variation in centripetal force is

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To calculate the change in centripetal force, use the formula:

[ F = \frac{m \cdot v^2}{r} ]

Where: ( F ) is the centripetal force, ( m ) is the mass of the train (4 kg), ( v ) is the velocity of the train (9 cm/s), ( r ) is the radius of the curvature.

- Calculate the initial centripetal force (( F_{\text{initial}} )) with the initial radius (36 cm).
- Calculate the final centripetal force (( F_{\text{final}} )) with the changed radius (24 cm).
- Find the difference ( \Delta F = F_{\text{final}} - F_{\text{initial}} ).

Substitute the values into the formula:

[ F_{\text{initial}} = \frac{4 , \text{kg} \cdot (9 , \text{cm/s})^2}{36 , \text{cm}} ]

[ F_{\text{final}} = \frac{4 , \text{kg} \cdot (9 , \text{cm/s})^2}{24 , \text{cm}} ]

[ \Delta F = F_{\text{final}} - F_{\text{initial}} ]

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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.

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