A model train with a mass of #8# #kg# is moving along a track at #12# #cms^-1#. If the curvature of the track changes from a radius of #45# #cm# to #240# #cm#, by how much must the centripetal force applied by the tracks change?

1 Answer
David G.
May 21, 2017

The change in magnitude of the centripetal force from before the change of radius to after is #0.256-0.048=0.208# #N#.

Explanation:

I'm going to work in metres, the SI unit of distance, rather than cm, because that will yield forces in newton (N) the SI unit of force. So, restating the question:

A model train with a mass of 8 kg is moving along a track at #0.12# # ms^−1#. If the curvature of the track changes from a radius of #0.45# #m# to #2.40# #m#, by how much must the centripetal force applied by the tracks change?

Centripetal force is given by:

#F = (mv^2)/r#

Before the change of radius, the centripetal force required is:

#F = (mv^2)/r = (8xx0.12^2)/0.45 = 0.256# #N#

After the change of radius, it is:

#F = (mv^2)/r = (8xx0.12^2)/2.4 = 0.0.048# #N#

The change in magnitude from before to after is #0.256-0.048=0.208# #N#.

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