A model train, with a mass of $5 k g$ $5 kg$ , is moving on a circular track with a radius of $3 m$ $3 m$ . If the train's rate of revolution changes from $\frac{1}{3} H z$ $1/3 Hz$ to $\frac{2}{9} H z$ $2/9 Hz$ , by how much will the centripetal force applied by the tracks change by?

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Answer 1 · 2018-03-20T17:22:27

The change in centripetal force is $= 36.56 N$ $=36.56N$

The centripetal force is

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

The mass of the train, $m = (5) k g$ $m=(5)kg$

The radius of the track, $r = (3) m$ $r=(3)m$

The frequencies are

$f_{1} = (\frac{1}{3}) H z$ $f_1=(1/3)Hz$

$f_{2} = (\frac{2}{9}) H z$ $f_2=(2/9)Hz$

The angular velocity is $ω = 2 π f$ $omega=2pif$

The variation in centripetal force is

$DeltaF=F_2-F_1$

$F_1=mromega_1^2=mr*(2pif_1)^2=5*3*(2pi*1/3)^2=65.80N$

$F_2=mromega_2^2=mr*(2pif_2)^2=5*3*(2pi*2/9)^2=29.24N$

$DeltaF=F_1-F_2=65.80-29.24=36.56N$

A model train, with a mass of 5 kg5kg5 kg, is moving on a circular track with a radius of 3 m3m3 m. If the train's rate of revolution changes from 1/3 Hz13Hz1/3 Hz to 2/9 Hz29Hz2/9 Hz, by how much will the centripetal force applied by the tracks change by?