# A model train, with a mass of 4 kg, is moving on a circular track with a radius of 15 m. If the train's kinetic energy changes from 32 j to 12 j, by how much will the centripetal force applied by the tracks change by?

Jun 10, 2017

$- \frac{8}{3} N$

Or using correct significant figures:

$- 2.7 N$

#### Explanation:

We know that the centripetal force on an object moving in a circle is:

${F}_{\text{cent" = m*a_"cent}} = \frac{m {v}^{2}}{r}$

And kinetic energy of an object is:

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

$\therefore 2 K E = m {v}^{2}$

We can substitute this into our first equation to give us:

${F}_{\text{cent}} = \frac{2 K E}{r}$

And therefore,

$\Delta {F}_{\text{cent}} = \frac{2 \Delta K E}{r} = \frac{2 \left(12 J - 32 J\right)}{15 m} = - \frac{40}{15} N = - \frac{8}{3} N$

Now, since the problem gives us 2 sig. figs, the answer needs 2 sig. figs as well.

$- 2.7 N$