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A model train with a mass of #4 kg# is moving along a track at #9 (cm)/s#. If the curvature of the track changes from a radius of #36 cm# to #45 cm#, by how much must the centripetal force applied by the tracks change?

Answer 1

Sebastian Acosta

The change in centripetal force is #=0.018N#

The centripetal force is

#vecF_C=(mv^2)/r*vecr#

The mass is of the train #m=4kg#

The velocity of the train is #v=0.09ms^-1#

The radii of the tracks are

#r_1=0.36m#

and

#r_2=0.45m#

The variation in the centripetal force is

#DeltaF=F_2-F_1#

The centripetal forces are

#||F_1||=4*0.09^2/0.36=0.09N#

#||F_2||=4*0.09^2/0.45=0.072N#

#DeltaF=F_1-F_2=0.09-0.072=0.018N#

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Answer 2

Charlotte Aaron

The centripetal force applied by the tracks must increase by approximately 5.0625 Newtons.

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Answer 3

Benjamin Asiedu

The centripetal force applied by the tracks must change by 0.5 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.