A model train, with a mass of #5 kg#, is moving on a circular track with a radius of #3 m#. If the train's rate of revolution changes from #1/2 Hz# to #2/8 Hz#, by how much will the centripetal force applied by the tracks change by?

1 Answer
Mar 16, 2018

Answer:

The change in centripetal force is #=111.03N#

Explanation:

The centripetal force is

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

The mass of the train, #m=(5)kg#

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

The frequencies are

#f_1=(1/2)Hz#

#f_2=(2/8)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=5*3*(2pi*1/2)^2=148.04N#

#F_2=mromega_2^2=mr*(2pif_2)^2=5*3*(2pi*1/4)^2=37.01N#

#DeltaF=F_1-F_2=148.04-37.01=111.03N#