Question

A model train, with a mass of `6 kg`, is moving on a circular track with a radius of `4 m`. If the train's kinetic energy changes from `24 j` to `42 j`, by how much will the centripetal force applied by the tracks change by?

Answer 1

`\deltaF_c=9N`

Explanation:

Given that we have the involvement of Kinetic energy and centripetal force.
Kinetic energy is given by the equation `K=1/2mv^2` and centripetal force by equation `F_c=mv^2/r`
From both equations, it can be seen that equation of kinetic energy can be substituted into the equation of centripetal force, and the equation would be `F_c=2K/r`

Given that we have to find just the change in the centripetal force, so `\deltaF_c=2/r\deltaK=2/r(K_f-K_i)`

`K_f=42J` and `K_i=24J`, `r=4m`
So, substituting into the equation `\deltaF_c=cancel{2}/cancel{4}^2*(42-24)=18/2=9N`

So the change in the centripetal force is given as above.