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A model train with a mass of #6 kg# is moving along a track at #8 (cm)/s#. If the curvature of the track changes from a radius of #3 cm# to #16 cm#, by how much must the centripetal force applied by the tracks change?

Answer 1

Lily Adams

#\DeltaF=1.04N#

#F_\circ=(mv^2)/r#

#\DeltaF = F_1-F_2=(mv^2)/r_1-(mv^2)/r_2=(6*0.08^2)/0.03-(6*0.08^2)/0.16=1.04N#

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Answer 2

Layla Ahmed

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

[F_{\text{centripetal}} = \frac{mv^2}{r}]

Where:

(m = 6 , \text{kg}) (mass of the train)
(v = 8 , \text{cm/s}) (velocity of the train)
(r_1 = 3 , \text{cm}) (initial radius)
(r_2 = 16 , \text{cm}) (final radius)

Using the formula with the initial radius (r_1) and then with the final radius (r_2), you can find the change in centripetal force by subtracting the initial force from the final force.

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Answer from HIX Tutor

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.