A model train with a mass of #5 kg# is moving along a track at #14 (cm)/s#. If the curvature of the track changes from a radius of #7 cm# to #24 cm#, by how much must the centripetal force applied by the tracks change?

Answer 1

A change of #Delta F=119/120=0.9916666" "#Newton

Given data: #v=14" "#cm/second#=0.14" "#meter/second #m=5" "#kilogram #r_1=7" "#centimeter#=.07" "#meter #r_2=24" "#centimeter#=0.24" "#meter

Formula for Centripetal Force

#F_1=(mv^2)/r_1=(5*(.14)^2)/(.07)=7/5" "#Newtons

#F_2=(mv^2)/r_2=(5*(.14)^2)/(.24)=49/120" "#Newtons

#F_1-F_2=Delta F=119/120=0.9916666" "#Newton

May God bless you all. I hope this explanation helps.

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Answer 2

Emily Abbate

The centripetal force must change by approximately 8.96 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.