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A model train with a mass of #2 kg# is moving along a track at #2 (cm)/s#. If the curvature of the track changes from a radius of #7 cm# to #1 cm#, by how much must the centripetal force applied by the tracks change?

Answer 1

Amelia Adams

The change in centripetal force is #=0.0686N#

The centripetal force is

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

The mass is of the train #m=2kg#

The velocity of the train is #v=0.02ms^-1#

The radii of the tracks are

#r_1=0.07m#

and

#r_2=0.01m#

The variation in the centripetal force is

#DeltaF=F_2-F_1#

The centripetal forces are

#||F_1||=2*0.02^2/0.07=0.0114N#

#||F_2||=2*0.02^2/0.01=0.08N#

#DeltaF=|F_1-F_2|=0.08-0.0114=0.0686N#

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Answer 2

Olivia Askew

The centripetal force applied by the tracks must increase by approximately 24.85 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.