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 `48` `J`, by how much will the centripetal force applied by the tracks change by?

Answer 1

Centripetal force changes from `8N` to `32N`

Explanation:

Kinetic energy `K` of an object with mass `m` moving at a velocity of `v` is given by `1/2mv^2`. When Kinetic energy increases `48/12=4` times, velocity is hence doubled.

The initial velocity will be given by `v=sqrt(2K/m)=sqrt(2xx12/4)=sqrt6` and it will become `2sqrt6` after increase in kinetic energy.

When an object moves in a circular path at a constant speed, it experiences a centripetal force is given by `F=mv^2/r`, where: `F` is centripetal force, `m` is mass, `v` is velocity and `r` is radius of circular path. As there is no change in mass and radius and centripetal force is also proportional to square of velocity,

Centripetal force at the beginning will be `4xx(sqrt6)^2/3` or `8N` and this becomes `4xx(2sqrt6)^2/3` or `32N`.

Hence centripetal force changes from `8N` to `32N`