A model train, with a mass of $3 k g$ $3 kg$ , is moving on a circular track with a radius of $2 m$ $2 m$ . If the train's rate of revolution changes from $\frac{2}{5} H z$ $2/5 Hz$ to $\frac{5}{6} H z$ $5/6 Hz$ , by how much will the centripetal force applied by the tracks change by?

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Answer 1 · 2017-12-04T10:32:22

The change in centripetal force is $= 501.1 N$ $=501.1N$

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, $r = 2 m$ $r=2m$

The frequencies are

$f_{1} = \frac{2}{5} = 0.4 H z$ $f_1=2/5=0.4Hz$

$f_{2} = \frac{5}{6} = 0.83 H z$ $f_2=5/6=0.83Hz$

The variation in centripetal force is

$DeltaF=F_2-F_1$

$F_1=mromega_1^2=mr*(2pif_1)^2=3*8*(2pi*0.4)^2=151.6N$

$F_2=mromega_2^2=mr*(2pif_2)^2=3*8*(2pi*0.83)^2=652.7N$

$DeltaF=F_1-F_2=652.7-151.6=501.1N$

A model train, with a mass of 3 kg3kg3 kg, is moving on a circular track with a radius of 2 m2m2 m. If the train's rate of revolution changes from 2/5 Hz25Hz2/5 Hz to 5/6 Hz56Hz5/6 Hz, by how much will the centripetal force applied by the tracks change by?