A model train with a mass of $4 k g$ $4 kg$ is moving along a track at $9 \frac{c m}{s}$ $9 (cm)/s$ . If the curvature of the track changes from a radius of $36 c m$ $36 cm$ to $45 c m$ $45 cm$ , by how much must the centripetal force applied by the tracks change?

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Answer 1 · 2018-02-18T14:56:59

The change in centripetal force is $= 0.018 N$ $=0.018N$

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 $m = 4 k g$ $m=4kg$

The velocity of the train is $v = 0.09 m s^{- 1}$ $v=0.09ms^-1$

The radii of the tracks are

$r_{1} = 0.36 m$ $r_1=0.36m$

and

$r_{2} = 0.45 m$ $r_2=0.45m$

The variation in the centripetal force is

$DeltaF=F_2-F_1$

The centripetal forces are

$||F_1||=4*0.09^2/0.36=0.09N$

$||F_2||=4*0.09^2/0.45=0.072N$

$DeltaF=F_1-F_2=0.09-0.072=0.018N$

A model train with a mass of 4 kg4kg4 kg is moving along a track at 9 (cm)/s9cms9 (cm)/s. If the curvature of the track changes from a radius of 36 cm36cm36 cm to 45 cm45cm45 cm, by how much must the centripetal force applied by the tracks change?