Question

A model train, with a mass of `4 kg`, is moving on a circular track with a radius of `3 m`. If the train's kinetic energy changes from `12 j` to `21 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 centripetal force is

`F=(mv^2)/r`

The kinetic energy is

`KE=1/2mv^2`

The variation of kinetic energy is

`Delta KE=1/2mv^2-1/2m u^2`

`=1/2m(v^2-u^2)`

The variation of centripetal force is

`DeltaF=m/r(v^2-u^2)`

`DeltaF=2m/r1/2(v^2-u^2)`

`=(2)/r*1/2m(v^2-u^2)`

`=(2)/r*Delta KE`

`=2/3*(21-12)N`

`=6N`

Answer 2

The change in centripetal force is `=6N`

Explanation:

The centripetal force is

`F=(mv^2)/r`

The kinetic energy is

`KE=1/2mv^2`

The variation of kinetic energy is

`Delta KE=1/2mv^2-1/2m u^2`

`=1/2m(v^2-u^2)`

The variation of centripetal force is

`DeltaF=m/r(v^2-u^2)`

`DeltaF=2m/r1/2(v^2-u^2)`

`=(2)/r*1/2m(v^2-u^2)`

`=(2)/r*Delta KE`

`=2/3*(21-12)N`

`=6N`