Question

A model train, with a mass of `8 kg`, is moving on a circular track with a radius of `2 m`. If the train's kinetic energy changes from `8 j` to `36 j`, by how much will the centripetal force applied by the tracks change by?

Answer 1

The centripetal force increases by 28 N, from 8 N to 36 N.
Details follow.

Explanation:

Centripetal force is given by

`F_c = (mv^2)/r`

For this train, we know the mass of the train, `m` and the radius `r` of the circular path it is following. What we need is the speed of the train `v`.

Since the kinetic energy `K` is given, we can use this to calculate the speed:

`K = 1/2 mv^2`

which I will rewrite as

`v^2 = (2 K)/m`

(because we will need `v^2` for the centripetal force formula, rather than `v`).

When the energy is 8 J, `v^2 = (2 *8)/8 = 2`

and the centripetal force is `F_c=(mv^2)/r= (8*2)/2 = 8 N`

When the energy is 36 J, `v^2 = (2 *36)/8 = 9`

and the centripetal force is `F_c=(mv^2)/r= (8*9)/2 = 36 N`

The change in centripetal force will be `36-8=28 N`