A model train with a mass of $7 k g$ $7 kg$ 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 $32 c m$ $32 cm$ to $36 c m$ $36 cm$ , by how much must the centripetal force applied by the tracks change?

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Answer 1 · 2018-03-25T07:05:59

The change in centripetal force is $= 0.035 N$ $=0.035N$

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 $m = 7 k g$ $m=7kg$

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

The radii of the tracks are

$r_{1} = 0.32 m$ $r_1=0.32m$

and

$r_{2} = 0.36 m$ $r_2=0.36m$

The variation in the centripetal force is

$DeltaF=F_2-F_1$

The centripetal forces are

$||F_1||=7*0.12^2/0.32=0.315N$

$||F_2||=7*0.12^2/0.36=0.280N$

$DeltaF=F_1-F_2=0.315-0.280=0.035N$

A model train with a mass of 7 kg7kg7 kg is moving along a track at 12 (cm)/s12cms12 (cm)/s. If the curvature of the track changes from a radius of 32 cm32cm32 cm to 36 cm36cm36 cm, by how much must the centripetal force applied by the tracks change?