Question

A model train with a mass of `8` `kg` is moving along a track at `12` `cms^-1`. If the curvature of the track changes from a radius of `45` `cm` to `240` `cm`, by how much must the centripetal force applied by the tracks change?

Answer 1

The change in magnitude of the centripetal force from before the change of radius to after is `0.256-0.048=0.208` `N`.

Explanation:

I'm going to work in metres, the SI unit of distance, rather than cm, because that will yield forces in newton (N) the SI unit of force. So, restating the question:

A model train with a mass of 8 kg is moving along a track at `0.12` `ms^−1`. If the curvature of the track changes from a radius of `0.45` `m` to `2.40` `m`, by how much must the centripetal force applied by the tracks change?

Centripetal force is given by:

`F = (mv^2)/r`

Before the change of radius, the centripetal force required is:

`F = (mv^2)/r = (8xx0.12^2)/0.45 = 0.256` `N`

After the change of radius, it is:

`F = (mv^2)/r = (8xx0.12^2)/2.4 = 0.0.048` `N`

The change in magnitude from before to after is `0.256-0.048=0.208` `N`.