# 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?

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.
$F = m {v}^{2} / r$
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