# A model train with a mass of 7 kg is moving along a track at 15 (cm)/s. If the curvature of the track changes from a radius of 24 cm to 45 cm, by how much must the centripetal force applied by the tracks change?

Jul 17, 2017

0.31N

#### Explanation:

First calculate the Centripetal Force for one of the situations, in this case I will calculate the force required for the 24cm track first.

At this stage you should convert your quantities to standards units, eg meters and meters per second.

So
$24$ cm = $0.24$m
$45$ cm = $0.45$m
$15$ cm/s = $0.15$m/s

Then use the formula:
${F}_{c} = \frac{m {v}^{2}}{r}$

And substitute the given values:
${F}_{c} = \frac{\left(7 k g\right) {\left(0.15 m {s}^{-} 1\right)}^{2}}{0.24 m} = 0.656 N$
${F}_{c} = \frac{\left(7 k g\right) {\left(0.15 m {s}^{-} 1\right)}^{2}}{0.45 m} = 0.350 N$

Now find the difference between the two forces:
$0.656 N - 0.350 N = 0.31 N$