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A model train, with a mass of #3 kg#, is moving on a circular track with a radius of #2 m#. If the train's rate of revolution changes from #2/5 Hz# to #3/7 Hz#, by how much will the centripetal force applied by the tracks change by?

Answer 1

Olivia Askew

The change in centripetal force is #0.19N#

Centripetal force is what

#F=mr omega^2#

#m=3kg#

#r=2m#

#Delta omega=(3/7-2/5)*2pi=2/35pirads^-1#

The centripetal force fluctuation is

#DeltaF=mr(Delta omega)^2#

#=3*2*(2/35pi)^2#

#=0.19N#

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Answer 2

Lily Adams

The change in centripetal force applied by the tracks can be calculated using the formula:

ΔF = m * Δω^2 * r

Where: ΔF = Change in centripetal force m = Mass of the train (3 kg) Δω = Change in angular velocity (final angular velocity - initial angular velocity) r = Radius of the circular track (2 m)

Substituting the given values:

ΔF = 3 kg * ((3/7 Hz)^2 - (2/5 Hz)^2) * 2 m

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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.