Question

A model train, with a mass of `4 kg`, is moving on a circular track with a radius of `6 m`. If the train's kinetic energy changes from `24 j` to `96 j`, by how much will the centripetal force applied by the tracks change by?

Answer 1

Mass of the train m= 4kg
The radius of circular path (r)=6m
Initial velocity,`v_1`
final velocity,`v_2`
Initial KE,`=1/2mv_1^2`
final KE,`1/2mv_2^2`
Change in KE =`1/2mv_2^2-1/2mv_1^2=96-24=72J`
Dividing both sides of this equation by radius (r)of circular path and multiplying both sides by 2 we have
`mv_2^2/r-mv_1^2/r=2*72/r`
We see that left side of the equation is the change in centripetal force
So The change in centripetal force is `=2*72/r=2.72/6(N.m)/m=24N`