Question

A model train with a mass of `9 kg` is moving along a track at `18 (cm)/s`. If the curvature of the track changes from a radius of `32 cm` to `45 cm`, by how much must the centripetal force applied by the tracks change?

Answer 1

`-0.26325N`

Explanation:

Centripetal (center-seeking) force is given by the equation

`F=(mv^2)/r`,

where `m` is mass, `v` is velocity and `r` is radius.

At the beginning, when the radius is `0.32m` and velocity `0.18ms^-1`, the centripetal force would be

`F=(9kg*0.0324m^2s^-2)/(0.32m)`
`0.91125N`

In the second part, when the radius has expanded to `0.45m`, centripetal force is

`F=(9kg*0.0324m^2s^-2)/(0.45m)`
`=0.648N`

The change in centripetal force is then found by simple subtraction,

`DeltaF=0.648N-0.91125N`
`=-0.26325N`