# 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?

Jul 27, 2016

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:

${F}_{1} = m {v}^{2} / {R}_{1}^{2} = 1 \text{ kg" cdot (0.06 " m/s")^2/(0.08 " m") = 4.5 cdot 10^(-2) " N}$

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:

${F}_{2} = m {v}^{2} / {R}_{2}^{2} = 1 \text{ kg" cdot (0.06 " m/s")^2/(0.09 " m") = 4.0 cdot 10^(-2) " N}$

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.