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?

1 Answer
Apr 3, 2016

Answer:

The change in centripetal force is # 20 N#.

Explanation:

To calculate centripetal force we need to use this equation:
#F= (mv^2) / r#
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 #E_k = ½ mv²#.

But notice that the equation for centripetal force has in it. That means we can take a shortcut by just working out from the kinetic energy equation and using that in the centripetal force equation.

That equation rearranged with as the subject is:
#v^2 =(2E_k)/m#

Initial velocity calculation:
#v_1^2 =(2 × 32)/8 = 8.00 m^2.s^(-2)#

Final velocity calculation:
#v_2^2 =(2 × 12)/8 = 3.00 m^2.s^(-2)#

Now work out the initial and final centripetal forces:
#F_1 = (mv_1^2) / r = (8 × 8.00) / 2 = 32 N#

#F_2 = (mv_2^2) / r = (8 × 3.00) / 2 = 12 N#

So the change in centripetal force is #32 – 12 = 20 N#.