A model train, with a mass of $4 k g$ $4 kg$ , is moving on a circular track with a radius of $6 m$ $6 m$ . If the train's kinetic energy changes from $16 j$ $16 j$ to $72 j$ $72 j$ , by how much will the centripetal force applied by the tracks change by?

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Answer 1 · 2018-02-16T07:10:46

The change in centripetal force is $= 18.67 N$ $=18.67N$

The centripetal force is

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

The kinetic energy is

$K E = \frac{1}{2} m v^{2}$ $KE=1/2mv^2$

The variation of kinetic energy is

$Delta KE=1/2mv^2-1/2m u^2$

$=1/2m(v^2-u^2)$

The mass is $m=kg$

The radius of the track is $r=6m$

The variation of centripetal force is

$DeltaF=m/r(v^2-u^2)$

$DeltaF=2m/r1/2(v^2-u^2)$

$=(2)/r*1/2m(v^2-u^2)$

$=(2)/r*Delta KE$

$=2/6*(72-16)N$

$=18.67N$

A model train, with a mass of 4 kg4kg4 kg, is moving on a circular track with a radius of 6 m6m6 m. If the train's kinetic energy changes from 16 j16j16 j to 72 j72j72 j, by how much will the centripetal force applied by the tracks change by?