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?

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Answer 1 · 2016-12-18T14:30:55

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

Centripetal force required for a circular path is found from

$F_c$ = $(mv^2)/r$

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

When travelling at $0.16 m/s$ on the track having $r = 0.48m$ , the required force is

$F_c$ = $(8 xx 0.16^2)/0.48$ = $0.427 N$

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

$F_c$ = $(8 xx 0.16^2)/1.2$ = $0.171 N$

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

A model train with a mass of 8 kg8 kg is moving along a track at 16 (cm)/s16 (cm)/s. If the curvature of the track changes from a radius of 48 cm48 cm to 120 cm120 cm, by how much must the centripetal force applied by the tracks change?