Question

A model train with a mass of `8 kg` is moving along a track at `16 (cm)/s`. If the curvature of the track changes from a radius of `48 cm` to `120 cm`, by how much must the centripetal force applied by the tracks change?

Answer 1

The centripetal force would decrease from 0.427 N to 0.171 N, a change of 0.256 N

Explanation:

Centripetal force required for a circular path is found from

`F_c` = `(mv^2)/r`

First, we should get rid of the centimetres! Convert both to metres to avoid conversion factor errors.

When travelling at `0.16 m/s` on the track having `r = 0.48m`, the required force is

`F_c` = `(8 xx 0.16^2)/0.48` = `0.427 N`

On the track having the greater radius, less force is required (note the `r` in the denominator)

`F_c` = `(8 xx 0.16^2)/1.2` = `0.171 N`

So, the change is centripetal force is `0.256 N`