Question

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?

Answer 1

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`