A model train, with a mass of 6 kg, is moving on a circular track with a radius of 7 m. If the train's rate of revolution changes from 4 Hz to 6 Hz, by how much will the centripetal force applied by the tracks change by?

1 Answer
Feb 7, 2016

$\Delta {F}_{c} = 672 {\pi}^{2}$

Explanation:

$\text{Centripetal force is given by: } {F}_{c} = m \cdot {\omega}^{2} \cdot r$
${\omega}_{1} = 2 \pi \cdot 4 = 8 \pi$
${\omega}_{2} = 2 \pi \cdot 6 = 12 \pi$
$\Delta \omega = 12 \pi - 8 \pi = 4 \pi$
$\Delta {F}_{c} = m \cdot \Delta {\omega}^{2} \cdot r$
$\Delta {F}_{c} = 6 \cdot {\left(4 \pi\right)}^{2} \cdot 7$
$\Delta {F}_{c} = 42 \cdot 16 {\pi}^{2}$
$\Delta {F}_{c} = 672 {\pi}^{2}$