# A model train, with a mass of 6 kg, is moving on a circular track with a radius of 4 m. If the train's kinetic energy changes from 24 j to 42 j, by how much will the centripetal force applied by the tracks change by?

Feb 17, 2016

$\setminus \delta {F}_{c} = 9 N$

#### Explanation:

Given that we have the involvement of Kinetic energy and centripetal force.
Kinetic energy is given by the equation $K = \frac{1}{2} m {v}^{2}$ and centripetal force by equation ${F}_{c} = m {v}^{2} / r$
From both equations, it can be seen that equation of kinetic energy can be substituted into the equation of centripetal force, and the equation would be ${F}_{c} = 2 \frac{K}{r}$

Given that we have to find just the change in the centripetal force, so $\setminus \delta {F}_{c} = \frac{2}{r} \setminus \delta K = \frac{2}{r} \left({K}_{f} - {K}_{i}\right)$

${K}_{f} = 42 J$ and ${K}_{i} = 24 J$, $r = 4 m$
So, substituting into the equation $\setminus \delta {F}_{c} = \frac{\cancel{2}}{\cancel{4}} ^ 2 \cdot \left(42 - 24\right) = \frac{18}{2} = 9 N$

So the change in the centripetal force is given as above.