# A model train, with a mass of 2 kg, is moving on a circular track with a radius of 3 m. If the train's kinetic energy changes from 4 j to 5 j, by how much will the centripetal force applied by the tracks change by?

Nov 1, 2017

The centripetal force will increase by a factor of 5/4.

#### Explanation:

The formulas for both kinetic energy
$K E = \frac{1}{2} \cdot m \cdot {v}^{2}$
and centripetal force
${F}_{c} = m \cdot {v}^{2} / r$
have a ${v}^{2}$ term. If the ${v}^{2}$ term used in the calculation of kinetic energy is increased by a factor of 5/4, the ${v}^{2}$ term used in the calculation of centripetal force will also increase by a factor of 5/4.

I hope this helps,
Steve