A model train with a mass of #7 kg# is moving along a track at #15 (cm)/s#. If the curvature of the track changes from a radius of #24 cm# to #45 cm#, by how much must the centripetal force applied by the tracks change?

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Answer 1 · 2017-07-17T02:51:03

0.31N

First calculate the Centripetal Force for one of the situations, in this case I will calculate the force required for the 24cm track first.

At this stage you should convert your quantities to standards units, eg meters and meters per second.

So
#24# cm = #0.24#m
#45# cm = #0.45#m
#15# cm/s = #0.15#m/s

Then use the formula:
#F_c = (mv^2)/r#

And substitute the given values:
#F_c = ((7 kg)(0.15m s^-1)^2)/(0.24 m) = 0.656 N#
#F_c = ((7 kg)(0.15m s^-1)^2)/(0.45 m) = 0.350 N#

Now find the difference between the two forces:
#0.656N - 0.350N = 0.31N#