# A model train with a mass of 8 kg is moving along a track at 16 (cm)/s. If the curvature of the track changes from a radius of 48 cm to 120 cm, by how much must the centripetal force applied by the tracks change?

Dec 18, 2016

The centripetal force would decrease from 0.427 N to 0.171 N, a change of 0.256 N

#### Explanation:

Centripetal force required for a circular path is found from

${F}_{c}$ = $\frac{m {v}^{2}}{r}$

First, we should get rid of the centimetres! Convert both to metres to avoid conversion factor errors.

When travelling at $0.16 \frac{m}{s}$ on the track having $r = 0.48 m$, the required force is

${F}_{c}$ = $\frac{8 \times {0.16}^{2}}{0.48}$ = $0.427 N$

On the track having the greater radius, less force is required (note the $r$ in the denominator)

${F}_{c}$ = $\frac{8 \times {0.16}^{2}}{1.2}$ = $0.171 N$

So, the change is centripetal force is $0.256 N$