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A model train, with a mass of #4 kg#, is moving on a circular track with a radius of #7 m#. If the train's kinetic energy changes from #8 j# to #42 j#, by how much will the centripetal force applied by the tracks change by?

Answer 1

Lily Adams

The change in centripetal force is #=9.71N#

The centripetal force is

#F=(mv^2)/r#

The kinetic energy is

#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=4kg#

The radius of the track is #r=7m#

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#

#=2/7*(42-8)N#

#=9.71N#

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Answer 2

Lily Adams

The change in kinetic energy of the train is 34 J. The centripetal force applied by the tracks will also change by 34 N.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.