A model train, with a mass of #4 kg#, is moving on a circular track with a radius of #4 m#. If the train's rate of revolution changes from #1/9 Hz# to #1/3 Hz#, by how much will the centripetal force applied by the tracks change by?

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Answer 1 · 2018-04-03T06:49:11

The change in centripetal force is #=62.38N#

The centripetal force is

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

The mass of the train, #m=(4)kg#

The radius of the track, #r=(4)m#

The frequencies are

#f_1=(1/9)Hz#

#f_2=(1/3)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=4*4*(2pi*1/9)^2=7.80N#

#F_2=mromega_2^2=mr*(2pif_2)^2=4*4*(2pi*1/3)^2=70.18N#

#DeltaF=F_2-F_1=70.18-7.80=62.38N#