Question

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?

Answer 1

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`