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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 #144 cm# to #360 cm#, by how much must the centripetal force applied by the tracks change?

Answer 1

Sebastian Acosta

The change i centripetal force is #0.024N#

Centripetal force is what

#F=(mv^2)/r#

The mass is of the train #m=1kg#

The velocity of the train is #v=0.24ms^-1#

The radii are

#r_1=1.44m#

additionally

#r_2=3.60m#

The centripetal force's variance is

#DeltaF=F_2-F_1#

What are the centripetal forces?

#F_1=1*0.24^2/1.44=0.04N#

#F_2=1*0.24^2/3.60=0.016N#

#DeltaF=0.04-0.016=0.024N#

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Answer 2

Julia Aguilar

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

ΔF = mv^2/Δr

Where: ΔF = change in centripetal force m = mass of the train (1 kg) v = velocity of the train (24 cm/s) Δr = change in radius (360 cm - 144 cm = 216 cm)

Substitute the values:

ΔF = (1 kg) * (24 cm/s)^2 / 216 cm ΔF ≈ 2.67 N

The centripetal force applied by the tracks must change by approximately 2.67 N.

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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.