# A model train, with a mass of 12 kg, is moving on a circular track with a radius of 6 m. If the train's kinetic energy changes from 120 j to 36 j, by how much will the centripetal force applied by the tracks change by?

Jun 1, 2016

$\setminus \Delta F = - 28$ N.

#### Explanation:

The centripetal force is defined as

$F = m {v}^{2} / r$

The kinetic energy is defined as

${E}_{k} = \frac{1}{2} m {v}^{2}$

So we can express the force as the energy writing

$F = 2 {E}_{k} / r$.

The initial force can be calculated with ${E}_{k} = 120$ J and radius $6$ m

${F}_{i} = 2 \cdot \frac{120}{6} = 40$ N

The final force can be calculated with ${E}_{k} = 36$ J and radius $6$ m

${F}_{f} = 2 \cdot \frac{36}{6} = 12$ N.

The difference of centripetal force is

$\setminus \Delta F = {F}_{f} - {F}_{i} = 12 - 40 = - 28$ N.

The negative sign is because the train is reducing the speed and then the centripetal force is reducing.