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 #5/6 Hz#, by how much will the centripetal force applied by the tracks change by?

Answer 1

Nora Arzate

The change in centripetal force is #=501.1N#

Centripetal force is what

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

The mass of the train, #m=(3)kg#

The radius, #r=2m#

The frequencies that are

#f_1=2/5=0.4Hz#

#f_2=5/6=0.83Hz#

The variation in centripetal force is

#DeltaF=F_2-F_1#

#F_1=mromega_1^2=mr*(2pif_1)^2=3*8*(2pi*0.4)^2=151.6N#

#F_2=mromega_2^2=mr*(2pif_2)^2=3*8*(2pi*0.83)^2=652.7N#

#DeltaF=F_1-F_2=652.7-151.6=501.1N#

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Answer 2

Charles Aeschliman

The centripetal force applied by the tracks will change by approximately 30 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.