# A model train with a mass of #1 kg# is moving along a track at #24 (cm)/s#. If the curvature of the track changes from a radius of #16 cm# to #150 cm#, by how much must the centripetal force applied by the tracks change?

The change in centripetal force is

Centripetal force is what

The centripetal force fluctuation is

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The centripetal force required for an object moving in circular motion is given by the formula:

( F_c = \frac{mv^2}{r} )

Where:

- ( F_c ) is the centripetal force,
- ( m ) is the mass of the object,
- ( v ) is the velocity of the object, and
- ( r ) is the radius of the circular path.

Initial centripetal force (( F_{c1} )) when the radius is 16 cm: ( F_{c1} = \frac{(1 , \text{kg}) \times (24 , \text{cm/s})^2}{16 , \text{cm}} ) ( F_{c1} = \frac{1 \times 576}{16} ) ( F_{c1} = \frac{576}{16} ) ( F_{c1} = 36 , \text{N} )

Final centripetal force (( F_{c2} )) when the radius is 150 cm: ( F_{c2} = \frac{(1 , \text{kg}) \times (24 , \text{cm/s})^2}{150 , \text{cm}} ) ( F_{c2} = \frac{1 \times 576}{150} ) ( F_{c2} = \frac{576}{150} ) ( F_{c2} = 3.84 , \text{N} )

Change in centripetal force: ( \Delta F_c = F_{c2} - F_{c1} ) ( \Delta F_c = 3.84 , \text{N} - 36 , \text{N} ) ( \Delta F_c = -32.16 , \text{N} )

The centripetal force applied by the tracks must decrease by ( 32.16 , \text{N} ) when the curvature of the track changes from a radius of 16 cm to 150 cm.

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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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