Question

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?

Answer 1

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 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:
`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`.