# 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?

Apr 3, 2016

The change in centripetal force is $20 N$.

#### Explanation:

To calculate centripetal force we need to use this equation:
$F = \frac{m {v}^{2}}{r}$
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:
${v}^{2} = \frac{2 {E}_{k}}{m}$

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.