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 #1/7 Hz#, by how much will the centripetal force applied by the tracks change by?

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Answer 1 · 2018-07-23T19:39:33

The change in centripetal force is #=39.88N#

The centripetal force is

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

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

The radius of the track, #r=(8)m#

The frequencies are

#f_1=(1/4)Hz#

#f_2=(1/7)Hz#

The angular velocity is #omega=2pif#

The variation in centripetal force is

#DeltaF=F_2-F_1#

#F_1=mromega_1^2=mr*(2pif_1)^2=3*8*(2pi*1/4)^2=59.22N#

#F_2=mromega_2^2=mr*(2pif_2)^2=3*8*(2pi*1/7)^2=19.34N#

#DeltaF=|F_2-F_1|=59.22-19.34=39.88N#