Question

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?

Answer 1

Let us apply the definition of centripetal force.

Explanation:

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:

`F = m v^2 / R`

With a radius of 8 cm, the centripetal force values:

`F_1 = m v^2 / R_1^2 = 1 " kg" cdot (0.06 " m/s")^2/(0.08 " m") = 4.5 cdot 10^(-2) " N"`

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:

`F_2 = m v^2 / R_2^2 = 1 " kg" cdot (0.06 " m/s")^2/(0.09 " m") = 4.0 cdot 10^(-2) " N"`

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.