# 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 1 Hz to 2 Hz, by how much will the centripetal force applied by the tracks change by?

Nov 18, 2016

The centripetal force applied is ${F}_{c} = 1654.8$Newtons.

#### Explanation:

Centripetal force is defined as ${F}_{c} = m r {\omega}^{2}$.
Angular acceleration $\omega = 2 \pi$(change in frequency)
$\implies \omega = 2 \pi \left({\nu}_{2} - {\nu}_{1}\right)$.
Now the centripetal force becomes
${F}_{c} = m r {\left[2 \pi \left({\nu}_{2} - {\nu}_{1}\right)\right]}^{2}$.
${F}_{c} = 4 m r {\pi}^{2} {\left({\nu}_{2} - {\nu}_{1}\right)}^{2}$
Substituting the given values we get,
${F}_{c} = 4 \left(2 k g\right) \left(7 m\right) {\left(3.14\right)}^{2} {\left[\left(2 H z\right) - \left(1 H z\right)\right]}^{2}$
$\therefore {F}_{c} = 1654.8$Newtons.