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A model train, with a mass of #7 kg#, is moving on a circular track with a radius of #3 m#. If the train's rate of revolution changes from #1/3 Hz# to #2/7 Hz#, by how much will the centripetal force applied by the tracks change by?

Answer 1

Emily Abbate

The change in centripetal force is #=24.44N#

Centripetal force is what

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

The mass of the train, #m=(7)kg#

The radius of the track, #r=(3)m#

The frequencies that are

#f_1=(1/3)Hz#

#f_2=(2/7)Hz#

The angular velocity is #omega=2pif#

The centripetal force fluctuation is

#DeltaF=F_2-F_1#

#F_1=mromega_1^2=mr*(2pif_1)^2=7*3*(2pi*1/3)^2=92.12N#

#F_2=mromega_2^2=mr*(2pif_2)^2=7*3*(2pi*2/7)^2=67.68N#

#DeltaF=F_2-F_1=92.12-67.68=24.44N#

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Answer 2

Carson Alexander

The centripetal force applied by the tracks will change by 27.64 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.