Question

A model train with a mass of `1 kg` is moving along a track at `4 (cm)/s`. If the curvature of the track changes from a radius of `160 cm` to `60 cm`, by how much must the centripetal force applied by the tracks change?

Answer 1

I found an increase of `0.002N`

Explanation:

Considering that centripetal force is:
`F_c=mv^2/r`
you see that, at constant velocity, a decrease in radius (in meters) will imply a increase of force; so:

`F_(c1)=mv^2/r_1=1*(0.04)^2/1.6=0.001N`
and
`F_(c2)=mv^2/r_2=1*(0.04)^2/0.6~~0.003N`
(everything in meters)

Centripetal force will increase of `0.002N`