A model train with a mass of #1 kg# is moving along a track at #24 (cm)/s#. If the curvature of the track changes from a radius of #72 cm# to #180 cm#, by how much must the centripetal force applied by the tracks change?

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Answer 1 · 2018-04-06T19:43:44

The change in centripetal force is #=0.048N#

The centripetal force is

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

The mass is of the train #m=1kg#

The velocity of the train is #v=0.24ms^-1#

The radii of the tracks are

#r_1=0.72m#

and

#r_2=1.80m#

The variation in the centripetal force is

#DeltaF=F_2-F_1#

The centripetal forces are

#||F_1||=1*0.24^2/0.72=0.08N#

#||F_2||=1*0.24^2/1.80=0.032N#

#DeltaF=F_1-F_2=0.08-0.0032=0.048N#