A model train, with a mass of #8 kg#, is moving on a circular track with a radius of #1 m#. If the train's rate of revolution changes from #5/8 Hz# to #5/4 Hz#, by how much will the centripetal force applied by the tracks change by?

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Answer 1 · 2017-03-04T20:50:42

#123.37N#

The centripetal force of an object is given by

#F = (mv^2)/r#

You can also find #v# by

#v = 2pirf#

where #f# is the frequency of revolution.

Substitute this into the above equation,

#F = (m(2pirf)^2)/r = (4mpi^2r^2f^2)/r#

#=4mrpi^2f^2#

or, since we're looking at the change in centripetal force from the change in frequency, then

#DeltaF = 4mrpi^2(Deltaf)^2#

where #Deltaf# is #5/4Hz - 5/8Hz = 5/8Hz#

Therefore, using the values that we know,

#DeltaF = 4xx8xx1xxpi^2xx(5/8)^2#

#= 123.37N#