A model train with a mass of #1 kg# is moving along a track at #6 (cm)/s#. If the curvature of the track changes from a radius of #8 cm# to #9 cm#, by how much must the centripetal force applied by the tracks change?
Let us apply the definition of centripetal force.
Centripetal force is exerted on curve trajectories to maintain their curvature; it is directed toward the center of the curve, and it is defined by:
With a radius of 8 cm, the centripetal force values:
where we have used SI units.
Now, with a radius of 9 cm, the centripetal force will decrease. Assuming that mass and speed are constant:
The explanation is very easy: the bigger the circle which the train describes is, the easier it is to maintain it on its trajectory, and the less force you must apply.