Question

A model train, with a mass of `3 kg`, is moving on a circular track with a radius of `3 m`. If the train's kinetic energy changes from `18 j` to `27 j`, by how much will the centripetal force applied by the tracks change by?

Answer 1

The change in centripetal force is `=6N`

Explanation:

The mass of the train is `m=3kg`

The radius of the track is `r=3m`

The centripetal force is

`F=(mv^2)/r`

`v^2=(Fr)/m`

The kinetic energy is

`KE=1/2mv^2`

Therefore,

The variation of kinetic energy is

`DeltaKE=1/2m(v_1^2-v_2^2)`

`v_1^2=(F_1r)/m`

`v_2^2=(F_2r)/m`

So,

`DeltaKE=1/2m((F_1r)/m-(F_2r)/m)=r/2(F_2-F_1)=r/2DeltaF`

`DeltaF=2/rDeltaKE`

The change in centripetal force is

`DeltaF=2/3*(27-18)=6N`