A model train with a mass of #9 kg# is moving along a track at #18 (cm)/s#. If the curvature of the track changes from a radius of #32 cm# to #45 cm#, by how much must the centripetal force applied by the tracks change?

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Answer 1 · 2016-04-17T09:53:24

#-0.26325N#

Centripetal (center-seeking) force is given by the equation

#F=(mv^2)/r#,

where #m# is mass, #v# is velocity and #r# is radius.

At the beginning, when the radius is #0.32m# and velocity #0.18ms^-1#, the centripetal force would be

#F=(9kg*0.0324m^2s^-2)/(0.32m)#
#0.91125N#

In the second part, when the radius has expanded to #0.45m#, centripetal force is

#F=(9kg*0.0324m^2s^-2)/(0.45m)#
#=0.648N#

The change in centripetal force is then found by simple subtraction,

#DeltaF=0.648N-0.91125N#
#=-0.26325N#