# A model train with a mass of 1 kg is moving along a track at 4 (cm)/s. If the curvature of the track changes from a radius of 160 cm to 60 cm, by how much must the centripetal force applied by the tracks change?

Jun 22, 2016

I found an increase of $0.002 N$

#### Explanation:

Considering that centripetal force is:
${F}_{c} = m {v}^{2} / r$
you see that, at constant velocity, a decrease in radius (in meters) will imply a increase of force; so:

${F}_{c 1} = m {v}^{2} / {r}_{1} = 1 \cdot {\left(0.04\right)}^{2} / 1.6 = 0.001 N$
and
${F}_{c 2} = m {v}^{2} / {r}_{2} = 1 \cdot {\left(0.04\right)}^{2} / 0.6 \approx 0.003 N$
(everything in meters)

Centripetal force will increase of $0.002 N$