# A model train with a mass of 4 kg is moving along a track at 21 (cm)/s. If the curvature of the track changes from a radius of 42 cm to 45 cm, by how much must the centripetal force applied by the tracks change?

The mass of the toy train $m = 4 k g$
The Velocity of the toy train $v = 21 c m {s}^{-} 1 = 0.21 m {s}^{-} 1$
The radius of first track = ${r}_{1} = 42 c m = 0.42 m$
The radius of second track = ${r}_{2} = 45 c m = 0.45 m$
$= m {v}^{2} \left(\frac{1}{r} _ 1 - \frac{1}{r} _ 2\right) = 4 \times {\left(0.21\right)}^{2} \times \left(\frac{1}{0.42} - \frac{1}{0.45}\right) N \approx .028 N$