# A model train with a mass of 3 kg is moving along a track at 12 (cm)/s. If the curvature of the track changes from a radius of 4 cm to 18 cm, by how much must the centripetal force applied by the tracks change?

Mar 19, 2016

=84000 #dyne

#### Explanation:

Let mass of train m =3kg = 3000 g
Velocity of train v = 12cm/s
Radius of first track ${r}_{1} = 4 c m$
Radius of Second track ${r}_{2} = 18 c m$
we know the centrifugal force =$\frac{m {v}^{2}}{r}$
Decrease in force in this case
$\frac{m {v}^{2}}{r} _ 1 - \frac{m {v}^{2}}{r} _ 2$
$= \left(m {v}^{2}\right) \cdot \left(\frac{1}{r} _ 1 - \frac{1}{r} _ 2\right) = 3 \cdot {10}^{3} \cdot {12}^{2} \left(\frac{1}{4} - \frac{1}{18}\right)$
$= 12000 \left(9 - 2\right) = 84000$dyne