Question

A model train, with a mass of `8` `kg`, is moving on a circular track with a radius of `1` `m`. If the train's kinetic energy changes from `32` `J` to `0` `J`, by how much will the centripetal force applied by the tracks change?

Answer 1

The centripetal force is given by `F=(mv^2)/r`, and we can calculate the change in `v` from the change in the kinetic energy, `E_k=1/2mv^2`. The change in the centripetal force acting is `-64` `N`.

Explanation:

The kinetic energy is given by `E_k=1/2mv^2`, and we can rearrange to make `v` the subject:

`v=sqrt((2E_k)/m)`

The final kinetic energy is zero and therefore the final velocity is zero.

We can use the mass, radius and initial kinetic energy to calculate the initial velocity:

`v=sqrt((2E_k)/m)=sqrt((2*32)/8) = sqrt (64/8) =sqrt8~~2.8` `ms^-1`

Since the final velocity is zero, the final centripetal force will be zero. The initial centripetal force will be:

`F=(mv^2)/r=(8*2.8^2)/1=64` `N`.

Since the final centripetal force is `0` `N`, the change in the centripetal force is:

final - initial = `0-64=-64` `N`