# A model train with a mass of #4 kg# is moving along a track at #6 (cm)/s#. If the curvature of the track changes from a radius of #32 cm# to #45 cm#, by how much must the centripetal force applied by the tracks change?

The change in centripetal force is

The centripetal force is

The radii of the tracks are

and

The variation in the centripetal force is

The centripetal forces are

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

ΔF = mv^2(1/r2 - 1/r1)

Where: ΔF is the change in centripetal force, m is the mass of the train (4 kg), v is the velocity of the train (6 cm/s), r2 is the final radius (45 cm), and r1 is the initial radius (32 cm).

Substituting the values:

ΔF = (4 kg)(6 cm/s)^2(1/45 cm - 1/32 cm)

ΔF ≈ (4 kg)(36 cm^2/s^2)(0.0222 - 0.03125)

ΔF ≈ (144 kg cm/s^2)(-0.00805)

ΔF ≈ -1.16 N

So, the centripetal force applied by the tracks must decrease by approximately 1.16 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.

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