Question

A model train, with a mass of `3` `kg`, is moving on a circular track with a radius of `3` `m`. If the train's kinetic energy changes from `18` `J` to `0` `J`, by how much will the centripetal force applied by the tracks change by?

Answer 1

The centripetal force is given by `F=(mv^2)/r`. We are given the mass and the radius and can calculate the velocity from the kinetic energy. The change is `-12` `N`.

Explanation:

The centripetal force on an object of mass `m` `kg` in circular motion at velocity `v` `ms^-1` in a circle of radius `r` `m` is given by:

`F=(mv^2)/r`

In this case we know the mass is `3` `kg` and the radius is `3` `m`, but the velocity is not immediately obvious. We are given the kinetic energy at two moments in time, though, and we know that kinetic energy is:

`E_k=1/2mv^2`

We can rearrange this to make `v` the subject:

`v=sqrt((2E_k)/m)`

Since the kinetic energy at the second time is `0` `J`, the velocity is also `0` `ms^-1`, and therefore the centripetal force is also `0` `N`.

At the first time, the kinetic energy is `18` `J`, so:

`v=sqrt((2*18)/3)=sqrt(36/3)=sqrt12` `ms^-1`

This means the centripetal force is:

`F=(mv^2)/r = (3*12)/3 = 12` `N` (since `(sqrt12)^2=12`)

So the centripetal force was `12` `N` at the beginning and `0` `N` at the end. Its change was therefore `-12` `N`.