# A model train with a mass of 8 kg is moving along a track at 9 (cm)/s. If the curvature of the track changes from a radius of 21 cm to 72 cm, by how much must the centripetal force applied by the tracks change?

Change in centripetal force
$\Delta F = 21 , 857.14286 \text{ }$Dynes

#### Explanation:

Given data:
$m = 8 \text{ }$kg
$v = 9 \text{ ""cm/sec}$

${r}_{1} = 21 \text{ ""cm}$
${r}_{2} = 72 \text{ ""cm}$

For Centripetal Force

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

${F}_{1} = \frac{m \cdot {v}^{2}}{r} _ 1 = \frac{8000 \cdot {9}^{2}}{21} = 30857.14286$

${F}_{2} = \frac{m \cdot {v}^{2}}{r} _ 2 = \frac{8000 \cdot {9}^{2}}{72} = 9000$

$\Delta F = {F}_{1} - {F}_{2} = 21 , 857.14286 \text{ }$Dynes

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