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A model train, with a mass of #3 kg#, is moving on a circular track with a radius of #8 m#. If the train's rate of revolution changes from #1/4 Hz# to #1/8 Hz#, by how much will the centripetal force applied by the tracks change by?

Answer 1

Amelia Adams

The change in centripetal force is #=44.4N#

Centripetal force is what

#F=(mv^2)/r=mromega^2N#

The mass, #m=(3)kg#

The radius, #r=8m#

The frequencies that are

#f_1=1/4=0.25Hz#

#f_2=1/8=0.125Hz#

The centripetal force fluctuation is

#DeltaF=F_2-F_1#

#F_1=mromega_1^2=mr*(2pif_1)^2=3*8*(2pi*0.25)^2=59.2N#

#F_2=mromega_2^2=mr*(2pif_2)^2=3*8*(2pi*0.125)^2=14.8N#

#DeltaF=F_1-F_2=59.2-14.8=44.4N#

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Answer 2

Carson Alexander

The centripetal force applied by the tracks will change by a factor of 4.

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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.