A model train, with a mass of #8 kg#, is moving on a circular track with a radius of #2 m#. If the train's kinetic energy changes from #32 j# to #12 j#, by how much will the centripetal force applied by the tracks change by?
The change in centripetal force is
To calculate centripetal force we need to use this equation:
m and r are both provided directly in the question. But in order to know the relevant velocities we need to calculate them from the kinetic energies that are provided using
But notice that the equation for centripetal force has v² in it. That means we can take a shortcut by just working out v² from the kinetic energy equation and using that in the centripetal force equation.
That equation rearranged with v² as the subject is:
Initial velocity calculation:
Final velocity calculation:
Now work out the initial and final centripetal forces:
So the change in centripetal force is