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A model train with a mass of #9 kg# is moving along a track at #18 (cm)/s#. If the curvature of the track changes from a radius of #66 cm# to #42 cm#, by how much must the centripetal force applied by the tracks change?

Answer 1

Benjamin Asiedu

The centripetal force changes by #=0.25N#

The centripetal force is

#F=(mv^2)/r#

mass, #m=9kg#

speed, #v=0.18ms^-1#

radius, #=(r) m#

The variation in centripetal force is

#DeltaF=F_2-F_1#

#F_1=mv^2/r_1=9*0.18^2/0.66=0.44N#

#F_2=mv^2/r_2=9*0.18^2/0.42=0.69N#

#DeltaF=0.69-0.44=0.25N#

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Answer 2

Julia Aguilar

The centripetal force must increase by approximately 6.74 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.