# A model train with a mass of 2 kg is moving along a track at 18 (cm)/s. If the curvature of the track changes from a radius of 9 cm to 3 cm, by how much must the centripetal force applied by the tracks change?

Jul 22, 2017

The change in centripetal force is $= 1.44 N$

#### Explanation:

The centripetal force is

$F = \frac{m {v}^{2}}{r}$

The mass is $m = 2 k g$

The speed is $v = 0.18 m {s}^{-} 1$

The radius is $= \left(r\right) m$

The variation in centripetal force is

$\Delta F = {F}_{2} - {F}_{1}$

${F}_{1} = m {v}^{2} / {r}_{1} = 2 \cdot {0.18}^{2} / 0.09 = 0.72 N$

${F}_{2} = m {v}^{2} / {r}_{2} = 2 \cdot {0.18}^{2} / 0.03 = 2.16 N$

$\Delta F = 2.16 - 0.72 = 1.44 N$