A model train with a mass of $3 k g$ $3 kg$ is moving along a track at $12 \frac{c m}{s}$ $12 (cm)/s$ . If the curvature of the track changes from a radius of $4 c m$ $4 cm$ to $8 c m$ $8 cm$ , by how much must the centripetal force applied by the tracks change?

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Answer 1 · 2018-03-09T15:18:48

The change in centripetal force is $= 0.54 N$ $=0.54N$

The centripetal force is

${\to F}_{C} = \frac{m v^{2}}{r} \cdot \to r$ $vecF_C=(mv^2)/r*vecr$

The mass is of the train $m = 3 k g$ $m=3kg$

The velocity of the train is $v = 0.12 m s^{- 1}$ $v=0.12ms^-1$

The radii of the tracks are

$r_{1} = 0.04 m$ $r_1=0.04m$

and

$r_{2} = 0.08 m$ $r_2=0.08m$

The variation in the centripetal force is

$DeltaF=F_2-F_1$

The centripetal forces are

$||F_1||=3*0.12^2/0.04=1.08N$

$||F_2||=3*0.12^2/0.08=0.54N$

$DeltaF=F_1-F_2=1.08-0.54=0.54N$

A model train with a mass of 3 kg3kg3 kg is moving along a track at 12 (cm)/s12cms12 (cm)/s. If the curvature of the track changes from a radius of 4 cm4cm4 cm to 8 cm8cm8 cm, by how much must the centripetal force applied by the tracks change?