Question

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?

Answer 1

The change in centripetal force is `=39.88N`

Explanation:

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`