A model train, with a mass of #12 kg#, is moving on a circular track with a radius of #6 m#. If the train's kinetic energy changes from #120 j# to #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.