# A model train, with a mass of 2 kg, is moving on a circular track with a radius of 4 m. If the train's kinetic energy changes from 16 j to 0 j, by how much will the centripetal force applied by the tracks change by?

Mar 1, 2016

$8$ Newtons

#### Explanation:

We can use kinetic energy formula to get the speed of the train before and after the kinetic energy change:

$v = \sqrt{\frac{2 E}{m}}$
$\to v = \sqrt{\frac{2 \cdot 16}{2}} = \sqrt{16} = 4$

So we know the train was travelling at $4 m {s}^{-} 1$

The kinetic energy at the end is $0 J$ so the train has obviously came to rest.

The centripetal force required at $4 m {s}^{-} 1$:

$F = \frac{m {v}^{2}}{r}$
$\to F = \frac{2 \cdot \left({4}^{2}\right)}{4} = 8 N$

And the centripetal force required when the train is at rest is just $0 N$. Thus the change in change in centripetal force is $8 - 0 = 8 N$