A model train with a mass of #1 kg# is moving along a track at #4 (cm)/s#. If the curvature of the track changes from a radius of #160 cm# to #60 cm#, by how much must the centripetal force applied by the tracks change?

Answer 1

I found an increase of #0.002N#

Considering that centripetal force is: #F_c=mv^2/r# you see that, at constant velocity, a decrease in radius (in meters) will imply a increase of force; so:

#F_(c1)=mv^2/r_1=1*(0.04)^2/1.6=0.001N# and #F_(c2)=mv^2/r_2=1*(0.04)^2/0.6~~0.003N# (everything in meters)

Centripetal force will increase of #0.002N#

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Answer 2

Xavier Adame

The centripetal force required for circular motion is given by the equation F = (m * v^2) / r, where m is the mass of the object, v is the velocity, and r is the radius of the curvature of the track.

Initial radius, r1 = 160 cm, final radius, r2 = 60 cm. Initial centripetal force, F1 = (m * v^2) / r1. Final centripetal force, F2 = (m * v^2) / r2.

Change in centripetal force = F2 - F1.

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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.