Question

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?

Answer 1

The change in centripetal force is `=62.38N`

Explanation:

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`