A model train, with a mass of $12 k g$ $12 kg$ , is moving on a circular track with a radius of $6 m$ $6 m$ . If the train's kinetic energy changes from $120 j$ $120 j$ to $36 j$ $36 j$ , by how much will the centripetal force applied by the tracks change by?

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Answer 1 · 2016-06-01T12:52:00

$\DeltaF=-28$ N.

The centripetal force is defined as

$F=mv^2/r$

The kinetic energy is defined as

$E_k=1/2mv^2$

So we can express the force as the energy writing

$F=2E_k/r$ .

The initial force can be calculated with $E_k=120$ J and radius $6$ m

$F_i=2*120/6=40$ N

The final force can be calculated with $E_k=36$ J and radius $6$ m

$F_f=2*36/6=12$ N.

The difference of centripetal force is

$\DeltaF=F_f-F_i=12-40=-28$ N.

The negative sign is because the train is reducing the speed and then the centripetal force is reducing.

A model train, with a mass of 12 kg12kg12 kg, is moving on a circular track with a radius of 6 m6m6 m. If the train's kinetic energy changes from 120 j120j120 j to 36 j36j36 j, by how much will the centripetal force applied by the tracks change by?