A model train with a mass of #4 kg# is moving along a track at #8 (cm)/s#. If the curvature of the track changes from a radius of #54 cm# to #27 cm#, by how much must the centripetal force applied by the tracks change?

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Answer 1 · 2017-03-04T20:33:25

#0.0474N#

Firstly let's just put everything in SI units - change the #cm# to #m# to make everything easier to solve.

#8cms^-1 = 0.08ms^-1#
#54cm = 0.54m#
#27 = 0.27m#

Now, the equation for centripetal force is

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

where #F# is force, #a# is acceleration, #m# is mass#, #v# is velocity# and #r# is radius.

In this case, the radius is changing, so we can say that

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

Putting in the values that we know,

#DeltaF = (4*0.08^2)/0.27 - (4*0.08^2)/0.54#

#= 0.0474N#