# A model train with a mass of #5 kg# is moving along a track at #12 (cm)/s#. If the curvature of the track changes from a radius of #32 cm# to #24 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 applied by the tracks must change according to the change in curvature of the track.

Using the formula for centripetal force:

F = (m * v^2) / r

Where: F = centripetal force m = mass of the train (5 kg) v = velocity of the train (12 cm/s) r = radius of curvature of the track

Initial centripetal force (F_initial) with a radius of 32 cm: F_initial = (5 kg * (12 cm/s)^2) / 32 cm

Final centripetal force (F_final) with a radius of 24 cm: F_final = (5 kg * (12 cm/s)^2) / 24 cm

Change in centripetal force: ΔF = F_final - F_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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