# A model train, with a mass of 2 kg, is moving on a circular track with a radius of 9 m. If the train's rate of revolution changes from 5 Hz to 2 Hz, by how much will the centripetal force applied by the tracks change by?

Apr 5, 2018

The change in centripetal force is $= 14922.9 N$

#### Explanation:

The centripetal force is

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

The mass of the train, $m = \left(2\right) k g$

The radius of the track, $r = \left(9\right) m$

The frequencies are

${f}_{1} = \left(5\right) H z$

${f}_{2} = \left(2\right) H z$

The angular velocity is $\omega = 2 \pi f$

The variation in centripetal force is

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

${F}_{1} = m r {\omega}_{1}^{2} = m r \cdot {\left(2 \pi {f}_{1}\right)}^{2} = 2 \cdot 9 \cdot {\left(2 \pi \cdot 5\right)}^{2} = 17765.3 N$

${F}_{2} = m r {\omega}_{2}^{2} = m r \cdot {\left(2 \pi {f}_{2}\right)}^{2} = 2 \cdot 9 \cdot {\left(2 \pi \cdot 2\right)}^{2} = 2842.4 N$

$\Delta F = {F}_{2} - {F}_{1} = 17765.3 - 2842.4 = 14922.9 N$