A model train with a mass of $5 k g$ $5 kg$ is moving along a track at $14 \frac{c m}{s}$ $14 (cm)/s$ . If the curvature of the track changes from a radius of $84 c m$ $84 cm$ to $21 c m$ $21 cm$ , by how much must the centripetal force applied by the tracks change?

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Answer 1 · 2017-12-17T12:56:05

The change in centripetal force is $= 0.35 N$ $=0.35N$

The centripetal force is

$F = \frac{m v^{2}}{r}$ $F=(mv^2)/r$

The mass is of the train $m = 5 k g$ $m=5kg$

The velocity is $v = 0.14 m s^{- 1}$ $v=0.14ms^-1$

The radii are

$r_{1} = 0.84 m$ $r_1=0.84m$

and

$r_{2} = 0.21 m$ $r_2=0.21m$

The variation in the centripetal force is

$DeltaF=F_2-F_1$

The centripetal forces are

$F_1=5*0.14^2/0.84=0.117N$

$F_2=5*0.14^2/0.21=0.467N$

$DeltaF=0.467-0.117=0.35N$

A model train with a mass of 5 kg5kg5 kg is moving along a track at 14 (cm)/s14cms14 (cm)/s. If the curvature of the track changes from a radius of 84 cm84cm84 cm to 21 cm21cm21 cm, by how much must the centripetal force applied by the tracks change?