Question

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?

Answer 1

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`