A model train, with a mass of $4 k g$ $4 kg$ , is moving on a circular track with a radius of $2 m$ $2 m$ . If the train's kinetic energy changes from $4 j$ $4 j$ to $15 j$ $15 j$ , by how much will the centripetal force applied by the tracks change by?

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Answer 1 · 2017-04-01T14:18:23

The centripetal force change by $= 11 N$ $=11N$

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 variation of centripetal force is

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

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

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

$=(2)/r*Delta KE$

$=2/2*(15-4)N$

$=11N$

A model train, with a mass of 4 kg4kg4 kg, is moving on a circular track with a radius of 2 m2m2 m. If the train's kinetic energy changes from 4 j4j4 j to 15 j15j15 j, by how much will the centripetal force applied by the tracks change by?