A model train, with a mass of $3 k g$ $3 kg$ , is moving on a circular track with a radius of $8 m$ $8 m$ . If the train's rate of revolution changes from $\frac{1}{4} H z$ $1/4 Hz$ to $\frac{1}{7} H z$ $1/7 Hz$ , by how much will the centripetal force applied by the tracks change by?

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Answer 1 · 2018-07-23T19:39:33

The change in centripetal force is $= 39.88 N$ $=39.88N$

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, $m = (3) k g$ $m=(3)kg$

The radius of the track, $r = (8) m$ $r=(8)m$

The frequencies are

$f_{1} = (\frac{1}{4}) H z$ $f_1=(1/4)Hz$

$f_{2} = (\frac{1}{7}) H z$ $f_2=(1/7)Hz$

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

The variation in centripetal force is

$DeltaF=F_2-F_1$

$F_1=mromega_1^2=mr*(2pif_1)^2=3*8*(2pi*1/4)^2=59.22N$

$F_2=mromega_2^2=mr*(2pif_2)^2=3*8*(2pi*1/7)^2=19.34N$

$DeltaF=|F_2-F_1|=59.22-19.34=39.88N$

A model train, with a mass of 3 kg3kg3 kg, is moving on a circular track with a radius of 8 m8m8 m. If the train's rate of revolution changes from 1/4 Hz14Hz1/4 Hz to 1/7 Hz17Hz1/7 Hz, by how much will the centripetal force applied by the tracks change by?