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A model train, with a mass of #6 kg#, is moving on a circular track with a radius of #2 m#. If the train's kinetic energy changes from #27 j# to #36 j#, by how much will the centripetal force applied by the tracks change by?

Answer 1

Nathan Ashcroft

The centripetal force changes by #=9N#

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 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*(36-27)N#

#=9N#

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Answer 2

Charlotte Aaron

The centripetal force applied by the tracks will change by 9 Newtons.

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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.