Question

A model train with a mass of `1 kg` is moving along a track at `6 (cm)/s`. If the curvature of the track changes from a radius of `12 cm` to `9 cm`, by how much must the centripetal force applied by the tracks change?

Answer 1

The change in the centripetal force is `=0.01N`

Explanation:

The centripetal force is

`vecF_C=(mv^2)/r*vecr`

The mass is of the train `m=1kg`

The velocity of the train is `v=0.06ms^-1`

The radii of the tracks are

`r_1=0.12m`

and

`r_2=0.09m`

The variation in the centripetal force is

`DeltaF=F_2-F_1`

The centripetal forces are

`||F_1||=1*0.06^2/0.12=0.03N`

`||F_2||=1*0.06^2/0.09=0.04N`

`DeltaF=F_2-F_1=0.04-0.03=0.01N`