A model train, with a mass of #6 kg#, is moving on a circular track with a radius of #2 m#. If the train's rate of revolution changes from #2 Hz# to #6 Hz#, by how much will the centripetal force applied by the tracks change by?

1 Answer
reudhreghs
Oct 9, 2017

The force will change by #15150N#

Explanation:

The equation for centripetal force is

#F_c = (mv^2)/r = momega^2r#

where #v# is linear velocity, #omega# is angular velocity, #r# is radius and #m# is mass.

We know that the mass is #6kg# and the radius is #2m#. We will use angular velocity for these calculations, but we could equally do it with linear velocity.

We know that

#omega = 2pif#

where #f# is the frequency, which we have.

For #f = 2Hz#

then

#omega = 2pi*2 = 12.6"rad"/"sec"#
#F_c = 6 * 12.6^2 * 2 = 1905N#

whereas with #f = 6Hz#

#omega = 2pif = 2pi * 6 = 37.7 "rad"/"sec"#

so

#F_c = 6 * 37.7^2 * 2 = 17055N#

Therefore the centripetal force will change by

#DeltaF_c = 17055N - 1905N = 15150N#

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