A model train, with a mass of #3 kg#, is moving on a circular track with a radius of #3 m#. If the train's kinetic energy changes from #18 j# to #27 j#, by how much will the centripetal force applied by the tracks change by?

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Answer 1 · 2018-05-09T08:37:10

The change in centripetal force is #=6N#

The mass of the train is #m=3kg#

The radius of the track is #r=3m#

The centripetal force is

#F=(mv^2)/r#

#v^2=(Fr)/m#

The kinetic energy is

#KE=1/2mv^2#

Therefore,

The variation of kinetic energy is

#DeltaKE=1/2m(v_1^2-v_2^2)#

#v_1^2=(F_1r)/m#

#v_2^2=(F_2r)/m#

So,

#DeltaKE=1/2m((F_1r)/m-(F_2r)/m)=r/2(F_2-F_1)=r/2DeltaF#

#DeltaF=2/rDeltaKE#

The change in centripetal force is

#DeltaF=2/3*(27-18)=6N#