A model train, with a mass of #4 kg#, is moving on a circular track with a radius of #15 m#. If the train's kinetic energy changes from #18 j# to #12 j#, by how much will the centripetal force applied by the tracks change by?

1 Answer
Daniel W.
Mar 19, 2016

Change in force :
# Δ F = F_1 - F_2 = 0.80 N#

Explanation:

The key thing in this question is to determine the change in velocity because the centripetal force depends on velocity.
#F=mv^2/r#
We can use the initial & final kinetic energies to determine initial and final velocities. And then determine the change in force.
(I'm actually going to take a shortcut and determine #v^2# with the kinetic energy and put that straight into the centripetal force equation.)

Initial
#E_k=½ mv^2 ⇒ v^2 = 2E_k/m#
#(v^2)_1 = 2 × 18 / 4 = 9.0#
#F=mv^2/r= 4/15 × v^2 = 0.2667 v^2#
#⇒ F_1 = 0.2667 × 9.0 = 2.4 N#
Final
#(v^2)_2 = 2 × 12 / 4 = 6.0#
#⇒ F_2 = 0.2667 × 6.0 = 1.6 N#

Change in force :
# Δ F = F_1 - F_2 = 0.80 N#

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