# A model train, with a mass of 4 kg, is moving on a circular track with a radius of 3 m. If the train's kinetic energy changes from 4 j to 15 j, by how much will the centripetal force applied by the tracks change by?

May 9, 2017

$\frac{22}{3} N$

#### Explanation:

we know that the change in kinetic energy of the system
$\Delta {E}_{k} = \frac{1}{2} m \left({v}_{f}^{2} - {v}_{i}^{2}\right)$

we also know that change in centripetal force is
centripetal force =$\frac{m {v}^{2}}{r}$ or change in centripetal force =$m \frac{{v}_{f}^{2} - {v}_{i}^{2}}{r}$
so we gonna substitute the values we get

$\left({v}_{f}^{2} - {v}_{i}^{2}\right) = 2 \cdot \Delta {E}_{k} / m = \frac{11}{2}$

we put this value in centripetal force change equation we get

$m \cdot \frac{11}{2} \cdot \frac{1}{r} = \frac{4 \cdot 11}{2 \cdot 3} = \frac{22}{3} N$