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A model train with a mass of #5 kg# is moving along a track at #4 (cm)/s#. If the curvature of the track changes from a radius of #16 cm# to #2 cm#, by how much must the centripetal force applied by the tracks change?

Answer 1

Charles Aeschliman

0.35N

We possess that:

This yields the centripetal force:

#F = (mv^2)/r#

Consequently, we can calculate the centripetal force change:

#DeltaF = F_2-F_1=(mv^2)/r_2 -( mv^2)/r_1#

#=((5)(0.04)^2)/0.02-((5)(0.04)^2)/0.16=0.35N#

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Answer 2

Benjamin Asiedu

The centripetal force applied by the tracks must change by a factor of 4.

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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.